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Hi I'm trying to advance a business date (28-12-2012) by 1 day and 1 week according to the Japan calendar.
import QuantLib as ql
trade_date = ql.Date(28, 12, 2012)
calendar = ql.Japan()
calendar.advance(trade_date, ql.Period('1D'))
Out[23]: Date(4,1,2013)
calendar.adva... |
Let’s say you do a 2s-10s steepener, dv01 neutral. What does this mean ? It means you are using the current dv01s of the 2s and 10s, which are approximately 1.99 and 9.12, to weight the relative principal amounts of the bonds. Now, the key point is, when the market moves, these dv01s move and you no longer have a ba... |
I read that before 2008, reserves of the banking system (vault cash and reserves at the Fed) fluctuated between \$40 billion and \$80 billion. However, as a result of quantitative easing, reserves exceeded \$2.5 trillion over the next 5 years. With such an increase in the magnitude of the reserves, one would think that... |
I read that before 2008, reserves of the banking system (vault cash and reserves at the Fed) fluctuated between \$40 billion and \$80 billion. However, as a result of quantitative easing, reserves exceeded \$2.5 trillion over the next 5 years. With such an increase in the magnitude of the reserves, one would think that... |
Look at the right side of the equation first. Earning can be treated as accumulated results for a relatively long period, which won't change too much if risk free rate increases. However, increasing risk free rate is gengerately accompanied by decreasing from capital market revaluation. For example, assume risk free is... |
Assume we have an insurance company that is valued under a risk-neutral probability measure. Further assume that the company, for simplicity, only has return smoothing based insurance. Assets return with the risk neutral rate while the insurance capital returns with the smoothing based return. The own funds are mutual ... |
I am looking into into AUD rates and I am a little confused. I tried to summarise below my doubts.
1) AUD FX swap implied rate = F/S-1 which is the rate payed to borrow AUD in the FX swap market. As I see from the chart it's expressed in bps and it's been mostly negative over the past 2 years. Does this mean y... |
I am looking into into AUD rates and I am a little confused. I tried to summarise below my doubts.
1) FX swap basis (difference between AUD FX swap implied rate and AUD OIS rate). Before covid-19 it has been mostly positive. Meaning it was more expensive to borrow in FX swap market than onshore?
times s... |
1) In FX swaps and FX forwards, the following formula holds:
$$S_{AUD/USD}(1+r_{USD})=(1+r_{AUD}+r_{basis})F_{AUD/USD}$$
The Spot $S_{AUD/USD}$ and the Forward $F_{AUD/USD}$ are traded and their prices are observed in the market. If you take the USD OIS rate for $r_{USD}$ and also the AUD OIS rate for $r_{AUD}$, ... |
1) In FX swaps and FX forwards, the following formula holds:
$$S_{AUD/USD}(1+r_{USD})=(1+r_{AUD}+r_{basis})F_{AUD/USD}$$
The Spot $S_{AUD/USD}$ and the Forward $F_{AUD/USD}$ are traded and their prices are observed in the market. If you take the USD OIS rate for $r_{USD}$ and also the AUD OIS rate for $r_{AUD}$, ... |
I found this model for floating rate bonds in a book I am reading and I am wondering if it is used anywhere in practice?
$$MV=\frac{\frac{(Index+QM)\cdot FV}{PER}}{\left(1+\frac{Index+DM}{PER}\right)^1}+\frac{\frac{(Index+QM)\cdot FV}{PER}}{\left(1+\frac{Index+DM}{PER}\right)^2}+\cdots+\frac{\frac{(Index+QM)\cdot FV... |
Most papers in the literature measure expected returns using the simple average of past returns. Why is this? When is it more correct to use geometric returns instead? Any good references?
I know that using log returns solves many of the issues with arithmetic/geometric returns, but not ideal to construct portfolios... |
Consider $d B_us(t)=r_{us} B_{us}(t) dt\\dX(t)=X(t)(r_{us}-r_J)dt+X(t)\sigma^T_J dW(t)\\d B_J(t)=r_{J} B_{J}(t) dt\\dS_J(t)=S_J(t)(r_J-\sigma^T_X\sigma_J)dt+S_J(t)\sigma^T_J dW(t)$
where the $\sigma$s are 2-dimensional vectors, but the Brownian motion is the same.
Consider a quanto put, whose payoff function is $... |
Consider $d B_{us}(t)=r_{us} B_{us}(t) dt\\dX(t)=X(t)(r_{us}-r_J)dt+X(t)\sigma^T_J dW(t)\\d B_J(t)=r_{J} B_{J}(t) dt\\dS_J(t)=S_J(t)(r_J-\sigma^T_X\sigma_J)dt+S_J(t)\sigma^T_J dW(t)$
where the $\sigma$s are 2-dimensional vectors, but the Brownian motion is the same.
Consider a quanto put, whose payoff function is... |
Consider $d B_{us}(t)=r_{us} B_{us}(t) dt\\dX(t)=X(t)(r_{us}-r_J)dt+X(t)\sigma^T_J dW(t)\\d B_J(t)=r_{J} B_{J}(t) dt\\dS_J(t)=S_J(t)(r_J-\sigma^T_X\sigma_J)dt+S_J(t)\sigma^T_J dW(t)$
where the $\sigma$'s are 2-dimensional vectors, but the Brownian motion is the same.
Consider a quanto put, whose payoff function i... |
I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio.
Would anyone please confirm that the global MVP is actuallay all-bond portfolio?
If that is true, then it will contradic... |
I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if bond is included as selectable asset.
Would anyone please confirm that the global MVP is actuallay all-bond portfolio in t... |
I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if **risk free bonds** (i.e, gvt bonds) is included as selectable asset.
Would anyone please confirm that the global MVP is a... |
I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if **risk free bonds** (i.e, gvt bonds) is included as selectable asset.
Would anyone please confirm that the global MVP is a... |
I have hourly open,high,low,close candles data for a particular asset. I wrote my own algo and some back testing code that replays the data from the past hourly candles to calculate the total return and total standard deviation. So let's say my set contains 30k hourly candles, I can run my code and replay only first 10... |
How to annualise hourly returns? |
It can be proved that risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{\mu_2 - \mu_1}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\sigma_2|$. so the equation is $\mu_P=\frac{\mu_2 - \mu_1}{\sigma_2+\sigma_1} \sigma_P +b$, I will get... |
Risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\sigma_2|$. so the equation is $\mu_P=\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1} \sigma_P +b$, I will get two values for $b... |
Risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\sigma_2|$ and $\omega_1+\omega_2=1$. so the equation is $\mu_P=\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1} \sigma_P +b$, I ... |
Risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\sigma_2|$ and $\omega_1+\omega_2=1$. so the equation is $\mu_P=\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1} \sigma_P +b$, I ... |
Risk-retun of 2-asset portfolio with perfect negative correlation $(\rho=-1)$ is a straight line with slope of $\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1}$ since $\sigma_P=|\omega_1\sigma_1 -\omega_2\sigma_2|$ and $\omega_1+\omega_2=1$. so the equation is $\mu_P=\frac{|\mu_2 - \mu_1|}{\sigma_2+\sigma_1} \sigma_P +b$, I ... |
The work of Breeden and Litzenberger-formula (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2642349) gives us a risk neutral probability distribution of a stock price, depending on the option prices.
---
**Question 1**: Is there a theoretical or practical way of obtaining real world probabilities given ris... |
Real world probabilities from option implied risk neutral density? |
Great question! Unfortunately, it's not easy. We can use option prices to get the $\mathbb{Q}$-distribution. However, the probability measure $\mathbb{Q}$ merges the stochastic discount factor (SDF) $M$ and the real world probabilities, $\mathbb{P}$, and it's not clear how to untangle the two (see [this answer](https:/... |
I'd like to simulate the expected payoff $\mathbb{E}[\Psi(L)]$ depending on the (stochastic) loss process $L$, when buying a CDO. I'm informed about the structure and how they work, yet I wonder of what nature this payoff function is or rather how I could construct such a payoff function?
When simulating it, does it... |
Problem: correlation between realized returns per trade and ex ante payoff is relatively low. Given that, it's possible that small (large) bets should be larger (smaller) than recommended by Kelly.
I have seen shrinkage estimators for Kelly which aim to take into account uncertainty about win rate and payoff but the... |
Hey in the COS method we use characteristic function of $\ln{S_T}$ to price european options (by recovering density from characteristic function). But how do we know that density exists? For example I would like to use this method to price options in Kou, NIG or CGMY model, do these Levy processes has density and we ca... |
Hey in the COS method we use characteristic function of $\ln{S_T}$ to price european options (by recovering density from characteristic function). But how do we know that density exists? For example I would like to use this method to price options in Kou, NIG or CGMY model, do these Levy processes has density and we ca... |
A bond is known to go **special** when its repo rate gets particularly low relative to the GC (General Collateral) repo rate.
In my mind, this can be caused by two scenarios:
**1. Institutional interest to short the bond**
Note *short* here is different to selling a bond that is already owned. In this scenario... |
Can both good buying and good selling cause a bond to go special on repo? |
According to the formula for pricing binary options with a volatility skew, it appears that the value of the binary option for a given strike gets lower, the higher the volatility skew at that strike. Why is this, intutively? I (think I) understand the derivation, but intuitively it seems like a positive volatility ske... |
Intuitive explanation for the value of a binary option being lower when volatility skew is positive? |
Not a lot can be done with graph theory / network analysis, but here is a little note http://jonathankinlay.com/2019/09/applications-graph-theory-finance/ (2019) showing how graphs can be used to visualize some data (a kind of a heatmap of a correlation matrix, looking for components and cliques).
Here is an older p... |
I am trying to understand how quasi-Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to prices an asset, but I am having a hard time combining what I have picked up from the resources I have read. For simplicity, I am just going to consider a European option on a single asset modelled by a scalar SDE $S_t... |
I have an ```N = 100``` covariance matrix. I am clustering the covariance matrix say into ```5 clusters```.
How can I compute the reduced covariance matrix of weighted cluster means which has ```dimension = 5x5```?
In particular, I am working on an algorithm for financial asset allocation. This algorithm first pe... |
How to reduce a covariance matrix after clustering? |
I have always estimated correlations and variances disjointly and later combine them to construct covariance matrices. Specifically, variances are estimated in a univariate setting (only using the data for each particular asset).
Is there any downside in this approach? Wondering if there is a benefit to estimate va... |
I am trying to understand how quasi-Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to prices an asset, but I am having a hard time combining what I have picked up from the resources I have read. For simplicity, I am just going to consider a European option on a single asset modelled by a scalar SDE $S_t... |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to prices an asset, but I am having a hard time combining what I have picked up from the resources I have read. For simplicity, I am just going to consider a European option on a single asset modelled by a scalar SDE $S_t... |
Sorry if this question is a little too basic but what determines repo rates? Not like "they are OTC transactions so they are determined directly between counterparties" but like what is the way you would approach calculations?
Take a bond priced $100$ at time $t=0$. Basic examples would say that party A lends party ... |
How are repo rates / repo haircuts determined? |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to prices an asset, but I am having a hard time combining what I have picked up from the resources I have read. For simplicity, I am just going to consider a European option on a single asset modelled by a scalar SDE $S_t... |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to prices an asset, but I am having a hard time combining what I have picked up from the resources I have read. For simplicity, I am just going to consider a European option on a single asset modelled by a scalar SDE $S_t... |
Of the courses I am taking in college this semester, two are Financial Mathematics and Derivatives. In each course, we learn different formulas to calculate the forward price of a forward contract. Obviously, the two formulas must equal each other, but I am not sure what the link is i.e. how to get from one formula to ... |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to prices an asset, but I am having a hard time combining what I have picked up from the resources I have read. I am just going to consider a European option on a single asset modelled by a simple scalar SDE $S_t=a(S_t,t)... |
**Background**\
I got a model for the distance-to-default of an instution in a system of banks from the paper "An SPDE model for systemic risk with endogeneous contagion". Therein they postulated that the empirical survival measure converges to a mean field limit. The SPDE describing this mean field limit depends on t... |
I have seen a few statements that link a particular annualised Sharpe Ratio to the likely frequency of 'loss day' across a given period:
*e.g. "A annualised Sharpe Ratio of X, implies the portfolio would suffer a down day Y times a month."*
What are the steps to go from a given Sharpe Ratio to the likely number ... |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to price an asset, but I am having a hard time understanding how. I am just considering a European option on a single asset modelled by a simple scalar SDE $S_t=a(S_t,t)\mathrm{d}t+b(S_t,t)\mathrm{d}W_t$. Here is what I u... |
Consider $$Z(t)=\left(\frac{S(t)}{H}\right)^p$$where $S$ has a standard Black-scholes Dynamics for a stock, $H$ is a postive constant and $p =1 - \frac{2r}{\sigma^2}$
and a simple claim with a pay-off at time T specified by pay-off function g. The arbitrate-free time t value is $$\pi^g(t)=e^{-r(T-t)}E^{\mathbb{Q}}_t... |
Is $E_t^{Q}(g(Y))=E_t^{Q^Z}(g(Y))$? |
I have two models of some spot. One is under local vol and the other is under stoch vol. Both are calibrated to the prevailing vanilla prices. I then consider the option that pays $1$ if the spot price exceeds a certain level before expiry, $T$. If there is any payment to be made, this happens at the time the barrier i... |
With reference to cross currency swaps, what does it mean to receive the basis?
"Demand from Japanese institutions to receive basis (USD funding) increased due to emergency dollar demand due to the financial crisis"
I understand basis is negative for most currencies vs. USD. So dollar lender in the swap pay... |
I generate 10000 random binomial paths for a stock whose price is from S(0) = 10 out to S(t) where t = 1 year. Assume geometric Brownian motion for the stock price with a drift of 15% per year and a volatility of 20%. I use 10000 equally spaced time steps of length along each path and $\Delta S = \mu S \Delta t \pm \si... |
In Euan Sinclair's book, Option Trading, he writes that $c <= S$, the price of a European call must be lower than the price of the underlying stock. To prove it, he applies the principle of no arbitrage:
> Imagine a European call is trading for more than the underlying. We then choose to sell the call and buy the u... |
### Combining Brownian bridges with quasi-Monte Carlo
> 1. How do I combine the BB and QMC ideas?
Brownian bridges is just a means of producing a Brownian path $W$, and Monte Carlo is a means by which we can evaluate expectations and integrals. Regular Monte Carlo would use a pseudo-random point set $U$ to estim... |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to price an asset, but I am having a hard time understanding how. I am just considering a European option on a single asset modelled by a simple scalar SDE $S_t=a(S_t,t)\mathrm{d}t+b(S_t,t)\mathrm{d}W_t$. Here is what I u... |
Warren Buffett has famously said that he could generate 50% annual returns if he was working with small sums of money. (He cannot move the needle enough now with large amounts of capital). Perhaps two reasons could explain this, holding his skill level fixed, 1) there are just more smaller companies and therefore more ... |
I have a series of log returns calculated on an index that is priced in Euro terms, and I'd like to convert those returns into USD terms. Would it be mathematically correct to calculate log returns on a USD/EUR exchange rate and just add the returns from the exchange rate to my Euro-denominated returns in order to succ... |
Given the asset price $S_t$ which is defined as follows
$$\frac{dS_t}{S_t}= r_tdt+\sigma_tdW_t$$
where $r_t$ **is not** necessarily deterministic.
What is the strategy of replication of for the portfolio with the payoff $\int_0^T \frac{dS_t}{S_t}$
?
**My attempt:**
In fact, I can solve this problem only ... |
I am trying to understand how quasi Monte Carlo (QMC) and the Brownian bridge (BB) can be combined to price an asset, but I am having a hard time understanding how. I am just considering a European option on a single asset modelled by a simple scalar SDE $S_t=a(S_t,t)\mathrm{d}t+b(S_t,t)\mathrm{d}W_t$. Here is what I u... |
I stumbled upon this job offer for Microstructure Performance Researcher and I didn't understand the parts below. (https://www.optiver.com/working-at-optiver/career-opportunities/2551339/)
Can you give me any examples of how knowing details about exchange connectivity, exchange protocols and market microstructure he... |
Usually tech companies/stocks are valued using one of the two methods:
DCF (discounted cash flows) method that is sensitive to interest rates raise (if rates up value down)
EBITDA or revenues multiples are sensitive to interest rates as cost of debt raises and profitability worsens if internet rates increase.
... |
How does VIX interpolate implied volatilities? |
Given the asset price $S_t$ which is defined as follows
$$\frac{dS_t}{S_t}= r_tdt+\sigma_tdW_t$$
where $r_t$ **is not** necessarily deterministic.
What is the strategy of replication of the portfolio with the payoff $\int_0^T \frac{dS_t}{S_t}$
?
**My attempt:**
In fact, I can solve this problem only for ... |
Consider a the Vascicek model, and let A and B denote the functions such that $P(t,T)=\exp(A(t,T)-B(t,T)r(t))$. We now look at a coupon bond that makes deterministic payments $\alpha_1,...,\alpha_N$ at dates $T_1,...,T_N$. Clearly the price of this coupon bond is $$\pi^c(t)=\sum_{i|T_i<t}\alpha_i P(t,T_i)$$.
Assume ... |
Consider a the Vascicek model, and let A and B denote the functions such that $P(t,T)=\exp(A(t,T)-B(t,T)r(t))$. We now look at a coupon bond that makes deterministic payments $\alpha_1,...,\alpha_N$ at dates $T_1,...,T_N$. Clearly the price of this coupon bond is $$\pi^c(t)=\sum_{i|T_i<t}\alpha_i P(t,T_i)$$.
Assume ... |
Given the asset price $S_t$ which is defined as follows
$$\frac{dS_t}{S_t}= r_tdt+\sigma_tdW_t$$
where $r_t$ **is not** necessarily deterministic.
What is the strategy of replication of the portfolio with the payoff $\int_0^T \frac{dS_t}{S_t}$
?
**My attempt:**
In fact, I can solve this problem only for ... |
I generate 10000 random binomial paths for a stock whose price is from S(0) = 10 out to S(t) where t = 1 year. Assume geometric Brownian motion for the stock price with a drift of 15% per year and a volatility of 20%. I use 10000 equally spaced time steps of length along each path and $\Delta S = \mu S \Delta t \pm \si... |
I am reading Shreve's Stochastic Calculus for Finance II. He states on pages 110 and 111 that,
$$E[exp(\sigma m-\frac{1}{2}\sigma^2 \tau_m)] = 1$$
$$E[exp(-\frac{1}{2}\sigma^2 \tau_m)] = e^{-\sigma m}$$
I understand that the top equation is a martingale and should thus have a constant expectation but I don't und... |
How to take the expectation of an exponential martingale? And an exponential with a random value? |
I stumbled upon this job offer for Microstructure Performance Researcher and I didn't understand the parts below. (https://www.optiver.com/working-at-optiver/career-opportunities/2551339/)
---
The parts I didn't understand:
> 1. This team is responsible for keeping Optiver ahead in the market by understanding... |
I am trying to forecast stock prices using Fast Fourier Transform, and plot historical, "future" (i.e. real) and forecast prices on the same chart to visually compare the accuracy of the forecasting method. However, I am puzzled as to why the output forecast values are much lower than the last input data of the time se... |
One buys out of money monthly call option and after a few days the trading volume goes down and the bid ask spread goes up. He sets a sell limit order based on the Black-Scholes equation but the order does not fill due to low volume. Then how can one sell the option with profit? Or this is not a good trading strategy. |
"why on the news it's usually mentioned that tech valuations are more negatively affected by an interest rates increase versus other sectors?"
It's specifically **long term interest rates** that affect tech/growth companies, since their earnings are supposed to be heavy weighted towards longer maturities.
If sho... |
One buys an OTM monthly call/put option and after a few days the trading volume goes down and the bid ask spread goes up. He sets a sell limit order based on the Black-Scholes equation but the order does not fill due to low volume. Then how can one sell the option with profit? Or this is not a good trading strategy. In... |
If I use every principal component to explain total variance of my portfolio, does it still make sense in portfolio optimization? Because since alpha factors try to find out and explain unexplained return by risk factors, if we explain whole part of return just by risk factors, what's the point of using alpha factors? ... |
How many principal components to use for statistical risk model? |
I was developing the binomial option pricing model via Python, according to the explanation given on [Wikipedia](https://en.wikipedia.org/wiki/Binomial_options_pricing_model). After computing the errors against the pricing of real options, I find an interesting observation: for ITM or ATM options, the pricing is valid ... |
Of the courses I am taking in college this semester, two are Financial Mathematics and Derivatives. In each course, we learn different formulas to calculate the forward price of a forward contract. Obviously, the two formulas must equal each other, but I am not sure what the link is i.e. how to get from one formula to ... |
I am learning from Bernt Oksendal's *Stochastic Differential Equations* and on page 276 Lemma 12.1.6, it is stated that:
The existence of an equivalent martingale measure $Q$ on the discounted price process $\overline{X}$ implies that the market is arbitrage-free.
A statement in the proof has come up, that I cann... |
A colleague mentioned the following: She wanted to look at some eurobonds in Reuters/Bloomberg to see if they if they "correctly break-out the swap curve and z-spread".
Would anyone understand what she is trying to say/do? Would be much appreciated |
OK I don't understand who "they" are supposed to be. Does "they" refer to Bloomberg/Refinitiv (your colleague is questioning whether Bloomberg/Refinitiv are right for this bond), or "they" refers to some other analytics, perhaps internal, that she wants to compare to Bloomberg/Refinitiv to see if they're in line?
Ge... |
Given the asset price $S_t$ which is defined as follows
$$\frac{dS_t}{S_t}= r_tdt+\sigma_tdW_t$$
where $r_t$ **is not** necessarily deterministic.
What is the strategy of replication of the portfolio with the payoff $\int_0^T \frac{dS_t}{S_t}$
?
**My attempt:**
In fact, I can solve this problem only for ... |
I am looking for reasonably up to date resources on global stock market valuations by country, using e.g. CAPE and PE. In the past I have used [this resource][1], but the updates have been discontinued (I have asked). Are there any other, roughly similar, resources?
[1]: https://www.starcapital.de/en/research/st... |
I am looking for reasonably up to date resources on global stock market valuations by country, using e.g. CAPE and PE. In the past I have used this resource: [starcapital.de][1], but the updates have been discontinued (I have asked). Are there any other, roughly similar, resources?
[1]: https://www.starcapital.d... |
I have been playing with option strategies in order to understand the advantages/drawbacks of all of them.
Then I realized this type of strategy is not so advertised in the web and cannot find any "academic" name for it.
The strategy consists in:
a) buy 2 deep OTM calls
b) buy 2 deep OTM puts
c) sell 1 OTM ca... |
How is this option strategy called? |
I'm reading the book of Clewlow and Strickland on Energy derivatives. In the section about the two-factor model, an equation, similar to B&S PDE is presented, but the proof is not presented.
Spot dynamics:
$$ dS=(r-\delta)S dt + \sigma S dW $$
Convenience yield dynamics:
$$ d\delta= \alpha(\hat{\delta}-\delta) d... |
Is there open-high-low-close data available at the daily timescale for yields? The data I can find from the Federal Reserve reports only one price, and moreover, I'm not sure when the data is reported. I know most bonds are not traded on exchanges, so it makes sense that this data is readily available, but I was wonder... |
OHLC Data for US Govt. Treasury Yields? |
I am reading Taleb's "Black Swan" (revised 2020th edition). In chapter 16 "The Aesthetics of Randomness" he describes the meaning of the exponent in the context of extrapolation. On page 265 there is a table (table 3) which depicts that if the exponent attains the value of $1$ then the share of the top $1$% will almost... |
I would like to check if a time-series follows an Ornstein-Uhlenbeck process defined by an SDE:
$$dX_t - \lambda (\mu - X_t) dt = \sigma dW_t$$
where
- $\lambda > 0$ is the mean-reversion coefficient
- $\mu$ is the long-term mean
- $\sigma>0$ is the variance
- $W_t$ is the Wiener process
This [paper][1] ... |
In a continuous setting, is it common to model stock prices using non-Markovian processes ? If so, do you have some examples of models ? Or is Markovianity something "embedded" in the continuous setting ? There is a lot of literature on diffusions processes, but what about non-Markovian financial models ? Any books/art... |
Do we model stock prices using non-Markovian processes in continuous setting? |
I am trying to forecast stock prices using Fast Fourier Transform, and plot historical, "future" (i.e. real) and forecast prices on the same chart to visually compare the accuracy of the forecasting method. However, I am puzzled as to why the output forecast values are much lower than the last input data of the time se... |
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