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I estimated a SML in terms of excess returns and i get the following parameters:
gamma0=0.0286
gamma1=0.0263
How can i give an economic interpretation of these two values? How they shape my model?
Thank you. |
My questions relates to this post https://quant.stackexchange.com/questions/36636/implying-risk-free-rates-using-put-call-parity , but I am using a different approach.
Given: ODAX Settlement prices across different maturities and strikes.
$$
PCP: p_{i,t,T} - c_{i,t,T} = (P_{t,T} - S_t) + e^{-r_{t,T}(T-t)}K_i
$$... |
I have a question that might appear simple for the more experienced here.
I'm trying to understand the concept behind short squeezes and i'm a little lost.
From what I understood:
Short selling consists of borrowing shares selling them and buying them back at a later point in time. The time when the shares... |
My questions relates to this post https://quant.stackexchange.com/questions/36636/implying-risk-free-rates-using-put-call-parity , but I am using a different approach.
***Given***: ODAX (Options on "DAX") Settlement prices across different maturities and strikes.
$$
PCP: p_{i,t,T} - c_{i,t,T} = (P_{t,T} - S_t) + e... |
I would like to normalise options:
1) Use **1 as stock_price** and scale **strike_price** accordingly, easy to do.
2) Use **same step for strike prices**. Different options have different step for strike prices, for one option step could be 10% (so strike prices for CALL will be 110%, 120% etc), for another optio... |
How to normalise options? Normalise strike price, premium, expiration |
Say I have a portfolio with two assets with weights (x, y), and the covariance matrix of the two asset is ((a, b)(b, a)). Then the total portfolio variance would be x^2a+2xyb+y^2a. It is easy to get that the percentage of the variance due to asset x is (x^2a+xyb)/(x^2a+2xyb+y^2a). I wonder in the n-dimensions cases, ho... |
I estimated a SML in terms of excess returns and I get the following parameters:
$\gamma_0=0.0286$
$\gamma_1=0.0263$
How can i give an economic interpretation of these two values? How they shape my model?
Note: In our assignment we have to deal with the following formula:
$$ R_i - R_f = \gamma_0 + \beta... |
Say I have a portfolio with two assets with weights (x, y), and the covariance matrix of the two asset is ((a, r)(r, b)). Then the total portfolio variance would be x^2a+2xyr+y^2b. It is easy to get that the percentage of the variance due to asset x is (x^2a+xyr)/(x^2a+2xyr+y^2b). I wonder in the n-dimensions cases, ho... |
My questions relates to this post https://quant.stackexchange.com/questions/36636/implying-risk-free-rates-using-put-call-parity , but I am using a different approach.
***Given***: ODAX (Options on "DAX") Settlement prices across different maturities and strikes.
$$
PCP: p_{i,t,T} - c_{i,t,T} = (P_{t,T} - S_t) + e... |
My questions relates to this post https://quant.stackexchange.com/questions/36636/implying-risk-free-rates-using-put-call-parity , but I am using a different approach.
***Given***: ODAX (Options on "DAX") Settlement prices across different maturities and strikes.
$$
PCP: p_{i,t,T} - c_{i,t,T} = (P_{t,T} - S_t) + e... |
> Is there a way to find out what the critical price of the stock
> approximately is at which point most shares were sold short?
Not that I am aware of, however, there is a way to find the Daily Short Sale Volume Ratio. Dividing the daily aggregate reported share volume of executed short-sale trades during regular... |
Say I have a portfolio with two assets with weights $(x, y)$, and the covariance matrix of the two asset is $((a, r)(r, b))$. Then the total portfolio variance would be $x^2a+2xyr+y^2b$. It is easy to get that the percentage of the variance due to asset $x$ is $\frac{x^2a+xyr}{x^2a+2xyr+y^2b}$. I wonder in the n-dimens... |
Can the Hodges-Tompkins adjustment (S. Hodges, R. Tompkins, *The Sampling Properties of Volatility Cones* 2000,2002 JoD) be used to de-bias any estimator computed from overlapping observations? It appears that most implementations apply it under the assumption of constant volatility. Is this adjustment applicable to es... |
I would like to **normalise options, to being able to compare it**. Make price of underlying symbol = 1, have same tenors, and same step for the strike price.
1) Use **1 as stock_price** and scale **strike_price** accordingly, easy to do.
2) Use **same step for strike prices**. Different options have different st... |
How to normalise options? Normalise strike price, premium, tenors |
I am trying to derive the **campbell shiller log linear relation,** and i got stuck with something (i believe) quite simple.
Before we are using the first-order tayler expansion is where i got stuck, because i can't figure out, how that $e$ got in there:
$\ln \left(1+\frac{D_{t+1}}{P_{t+1}}\right)=\ln \left(1+\exp ... |
I am trying to understand the abbreviations in the Bloomberg European stock or STOXX data. Each ticker represents **company name abbreviation - Listed exchange**.
For example, CSP - LN is Countryside Properties PLC - **London stock exchange**. I am hoping to find a document where I can get the **"two-letter"** abbr... |
I'm looking for a way of getting free historical daily market caps ? I can get todays Market cap from yahoo but need old market caps also.. thanks for the help |
I'm looking for a way of getting free historical daily market caps ? I can get todays Market cap from yahoo but need old market caps also.. thanks for the help.
ps: I don't have Bloomberg and school doesn't provide us with any data provider access. |
Tiingo.com has [fundamental data][1] available through an [API][2] you can access using Python. I'm not sure if you have to pay for it or if it's included with a free account. Either way, the outstanding shares are on the balance sheet within the fundamental data you can get through their REST API.
YCharts has thi... |
Lets say one wants to use straddles to "go long vol". Is there any way to give general properties of the different lengths of expiry of such a strategy. Or general pros and cons of having longer vs shorter.
Or does this depend to much on sentiment? |
Tiingo.com has [fundamental data][1] available through an [API][2] you can access using Python. I'm not sure if you have to pay for it or if it's included with a free account. Either way, the outstanding shares are on the balance sheet within the fundamental data you can get through their REST API.
YCharts has thi... |
Tiingo.com has [fundamental data][1] available through an [API][2] you can access using Python. I'm not sure if you have to pay for it or if it's included with a free account. Either way, the outstanding shares are on the balance sheet within the fundamental data you can get through their REST API.
YCharts has thi... |
[Example 2 of this Wiki article on](https://en.wikipedia.org/wiki/Risk-neutral_measure#Example_2_%E2%80%93_Brownian_motion_model_of_stock_prices) the risk-measure describes how a stock price $S_t$ that is modeled with Geometric Brownian motion with drift $\mu$
$$
dS_t = \mu S_t dt + \sigma S_t dW_t
$$
can be rewrit... |
I need to price a callable Equity Return Swap by Accrual. ERS has property callable T+1 and I don't get it. Does it mean that when a call happen we fix a price that and pay Accrual the next day? Could you please go over it a bit?
The structure is Fixed leg vs Equity leg |
I am trying to understand how pairs trading works but I am confused about how to go about calculating the return on the pairs trade when I reverse my positions. I have been reading 'Pairs Trading - Quantitative methods and analysis' by Ganapathy Vidyamurthy. My understanding is limited at this time, although the whole ... |
I stumbled upon the following sentences many times in different papers, all describing an approach for the same experiment: They try to calculate sensitivities (Beta) for different stocks via regression to then sort them into different buckets (portfolios). The papers say:
"For each stock we estimate factor loadings... |
In a 1-period binomial model, with initial stock price 100, if the stock price is either 50,100, or 150 after 1 period then how can I show there is no longer a unique no-arbitrage price for a European call option with strike price K=150. What would the range of values for this price be that ensure there is no arbitrage... |
# Systematically finding most liquid futures instruments
-----
## Can we put together a better list than the academic articles?
Yes! The lists in existing publications [[1][koijen], [2][han]] are great, but fall slightly short of your goal:
>I'm asking for a **systematic**, **repeatable** procedure for det... |
So, I read the following.
"we can construct a 5 year swap using 3 month libor combined with a 3mo-4.75yr forward swap, weighted by the dv01s of each part"
I am not sure I understand how this is the case.
Can someone please explain?
Thanks |
>A stock's price movement is described by the equations $dS_t=0.02S_tdt+0.25S_tdW_t$ and $S_0=100$. An investor buys a call option on said stock with a strike price $K=95$ which expires in $T=2$ years. What is the probability that the investor makes a profit greater than $20$ at expiry? The risk-free rate is $2\%$ (con... |
The following Clojure code correctly outputs the table in the similar 4.19.6, but I'm wildly out on the asymmetrical.
```
(defn double-barrier-binary
[S L U T r b v asymmetric?]
(let [R 1
Z (Math/log (/ U L))
v-sq (Math/pow v 2)
term (- (/ (* 2 b) v-sq) 1)
alpha (* -0.5 ter... |
I read the following statement:
> We can construct a 5 year swap using 3 month libor combined with a 3mo-4.75yr forward swap, weighted by the dv01s of each part.
I am not sure I understand how this is the case.
Can someone please explain?
Thanks |
I'm thinking of writing a master's thesis about pricing options using levy processes, but I wonder if these processes are actually used to model stock prices or not (and which specifically)? And if not which ones are used? In addition, I wonder if it is difficult to implement the right code in python or can it be done ... |
I'm thinking of writing a master's thesis about pricing options using Levy processes, but I wonder if these processes are actually used for modeling stock prices or not (and which specifically)? And if not which ones are used?
In addition, I wonder if it is difficult to implement the right code in Python or can it ... |
Which process is the most commonly used for modeling stock prices? |
The following Clojure code correctly outputs the table in section 4.19.6 of "The Complete Guide to Option Pricing Formulas", but I'm wildly out on the asymmetrical in 4.19.7.
```
(defn double-barrier-binary
[S L U T r b v asymmetric?]
(let [R 1
Z (Math/log (/ U L))
v-sq (Math/pow v 2)
... |
Mid price is so noisy so I try to use the weighted price, which is much better.
However I want to define a better price called micro-price. I use different level of quote and give the different parameter to the multi-level price, however I can't get a better price than the weighted price.
**My questions are:**
... |
Mid price is so noisy so I try to use the weighted price, which is much better.
However I want to define a better price called micro-price. I use different level of quote and give the different parameter to the multi-level price, however I can't get a better price than the weighted price.
**My questions are:**
... |
Mid price is so noisy so I try to use the weighted price, which is much better.
However I want to define a better price called micro-price. I use different level of quote and give the different parameter to the multi-level price, however I can't get a better price than the weighted price.
**My questions are:**
... |
Mid price is so noisy so I try to use the weighted price, which is much better.
However I want to define a better price called micro-price. I use different level of quote and give the different parameter to the multi-level price, however I can't get a better price than the weighted price.
**My questions are:**
... |
I've been calling this ratio "acceleration" in my head, so I'll do the same in this post. The question is, is this relationship used anywhere and if so, how? My thought process is as follows.
Risk is typically quantified through standard deviation. But how good of a proxy for risk is SD really? Upside deviation is no... |
I have started an analyst role and I am trying to familiarize myself with the Black-Scholes formula in VBA to gauge option prices.
However, I cannot seem to get the Put Theta to work properly. I have split the complex formula into different parts (not the most elegant solution, but it helps me find the error quicker... |
We have used it as a criterion for portfolio selection, for example in [An Empirical Analysis of Alternative Portfolio Selection Criteria][1] and [Risk-Reward Optimisation for Long-Run Investors: An Empirical Analysis][2].
What we found there, however, is that reducing the downside was more important than increasing t... |
I'm running a simulation for a 5 asset portfolio, calculating the optimal weights of each asset both with the statistical model (i.e. single index) and with the CAPM. my question is: how do you compute the covariance matrix in the CAPM? should I use the beta of each stock or the w% invested in each stock?
|
I have started an analyst role and I am trying to familiarize myself with the Black-Scholes formula in VBA to gauge option prices.
However, I cannot seem to get the Put Theta to work properly. I have split the complex formula into different parts (not the most elegant solution, but it helps me find the error quicker... |
I have started an analyst role and I am trying to familiarize myself with the Black-Scholes formula in VBA to gauge option prices.
However, I cannot seem to get the Put Theta to work properly. I have split the complex formula into different parts (not the most elegant solution, but it helps me find the error quicker... |
Covid-19 and similar risks are low probability, high loss events. Does it make sense to utilize options to provide hedges for such events? For example, should one utilize long positions in deep out-of-the-money puts as a hedge to such catastrophic events? It seems to me that such positions provide the similar risk a... |
Covid-19 and similar risks are low probability, high loss events. Does it make sense to utilize options to provide hedges for such events? For example, should one utilize long positions in deep out-of-the-money puts as a hedge to such catastrophic events? It seems to me that such positions provide the similar risk a... |
Covid-19 and similar risks are low probability, high loss events. Does it make sense to utilize options to provide hedges for such events? For example, should one utilize long positions in deep out-of-the-money puts as a hedge to such catastrophic events? It seems to me that such positions provide the similar risk a... |
I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows:
Stage 1:
$$z_t= a+ bX_t+e_t$$
Stage 2:
$$ \Delta z_t = \alpha_1 (z_{t-1}-a-bX_{t-1}) + \gamma_{11} \Delta z_{t-1} + \gamma_{12} \Delta X_{t-1} +\var... |
I have a VECM model that Im using to determine the revenues for a firm, based on factors like Interest rates, S&P 500 and company specific variables, as follows:
Stage 1:
$$z_t= a+ bX_t+e_t$$
Stage 2:
$$ \Delta z_t = \alpha_1 (z_{t-1}-a-bX_{t-1}) + \gamma_{11} \Delta z_{t-1} + \gamma_{12} \Delta X_{t-1} +\var... |
**There's no easy answer to your question**, as noob2 pointed out. You can **look online for info from Universa**. That fund does exactly what you are asking: https://www.universa.net/riskmitigation.html Of course, post a crash, such as the one we just experienced, the cost of hedges is larger than it is prior to s... |
I am trying to calculate NAV and performance for a L/S fund which shorts via CFD. Obviously in a traditional short sale, there would be cash generated to match liability incurred but this is not the case with CFD short. Any help with how to account for it? And likewise how to measure portfolio return? |
Given some broker costs today. What is the best way to extrapolate them into the history ? Would it be linear or exponential rise (towards history) ? |
Given some broker costs today. What is the best way to extrapolate them into the history ? Would it be linear or exponential rise (towards history) ?
This would be for backtest simulation involving multi-asset class futures, to incorporate appropriate broker costs. Not looking for price impacts in transactions. |
One of the most straighforward way to hedge tail risk and buy insurance is just buying the Vix. A few hedge funds made a lot of money on the [VIX lately][1].
What's the downside? Well in normal times (which are most of them) you actually need to pay for that insurance. That's called the variance risk premium.
So... |
I have also been looking into this stuff for a while. Apparently there are not that many tail risk funds, the prominent ones being Taleb and Spitznagel's Universa and Bhansali's LongTail Alpha. Obviously, all these guys have tons of papers and books on this topic. Spitznagel provides some nice case study on prototypica... |
I would like to know the what the relationship is between the time value of call/puts. From the put call parity formula $C-P = S_{t} - PV(K)$ and that call/put options is simply the sum of the intrinsic and time values. Does that then imply that the no-arbitrage relationship of the time value of $C$ is equal to the tim... |
I am trying to calculate NAV and performance for a L/S fund which shorts via CFD. Obviously in a traditional short sale, there would be cash generated to match liability incurred but this is not the case with CFD short.
**Any help with how to account for it? And likewise how to measure portfolio return?** |
How to calculate long-short performance using CFDs? |
I would like to know what the relationship is between the time value of call/puts. From the put call parity formula
$$C-P = S_{t} - PV(K)$$
and that value of call/put options is simply the sum of the intrinsic and time values
$$C=(S-K)^++TV_C$$
$$P=(K-S)^++TV_P$$
Does that then imply that the no-arbitrage... |
I'm trying to understand the derivation of Ito's process with respect to a Forward $F$ on a stock $S$ that pays a constant dividend yield, say $y$. Stock follows brownian motion $\\$
$dS_{t} = S_{t}(\mu dt + \sigma dW_{t})$ $\\$ and $r$ is interest rate.
Can someone verify that the Ito's process of $F$ is the follo... |
I am unsure about the quantities to keep in the risky asset, S, and the non-risky asset, M, when constructing an insured portfolio via Call + Cash (rather than Stock + Put). My understanding so far is below.
In a Black-Scholes framework trading 2 unrelated securities S (stock) and M (money market) and assuming no ar... |
Insured Portfolio via call + cash: how much cash? |
I am unsure about the quantities to keep in the risky asset, S, and the non-risky asset, M, when constructing an insured portfolio via Call + Cash (rather than Stock + Put). My understanding so far is below.
In a Black-Scholes framework trading 2 unrelated securities S (stock) and M (money market) and assuming no ar... |
I am unsure about the quantities to keep in the risky asset, S, and the non-risky asset, M, when constructing an insured portfolio via Call + Cash (rather than Stock + Put). My understanding so far is below.
In a Black-Scholes framework trading 2 unrelated securities S (stock) and M (money market) and assuming no ar... |
I am well aware of how the ordinary Black and Scholes equation is derived, under the assumption of an arbitrage free portfolio, $V=G-hS$. Here $S$ is the price of the underlying and $G$ is the option price. Suppose now that the portfolio is stochastic, and follows the process
$$(1): dV=rVdt+f(V,t)VdW,$$
where $r$ is ... |
Let's say I have a return forecast for each stock in the DAX index. I also have a covariance matrix for these 30 stocks.
I want to solve for the 30 weights by maximising the forecast portfolio return, subject to keeping the overall volatility at a certain target level, and subject to multiple tracking error constra... |
Multiple tracking error constraints - is this problem convex? |
As I understand it, recovery swaps and CDS are both used to provide hedging against the default risk of a loan.
What is the difference between them? |
I am aware that this is a simple question; but, given the scenario below, I have not found a satisfying answer while searching this site or Google.
**My understanding**
*Stock options* have been described as purchasing a contract that is valid for a limited time frame and gives you the 'option, but not the obliga... |
What is the benefit of buying stock options vs. purchasing stock? |
how can we expand this sum? $\sum_{i=1}^n (e^{rt_i-\frac{1}{2}\sigma^2t_i+\sigma w_{t_i}})^2$ where: $w_{t_i}$ is a standard brownian motion
if we let $m_t=e^{-\frac{1}{2}\sigma^2t_i+\sigma w_{t_i}}$ is a martingale where $m_0$ = 1, why does it reduce to $\sum_{i,j=1}^n e^{r(t_i+t_j)+\sigma^2\;min(t_i, t_j)}$
i k... |
I'm currently dealing with the following question:
**In Asset Pricing, well-informed investors know about the concept of the efficient frontier. Does this mean that they only invest in portfolios that lie on this efficient frontier?** I have that
$E[R^i]=R^f - \rho_{m, R^i} \sigma[R^i]\frac{\sigma[m]}{E[m]}$
... |
Asset Pricing and Stochastic Discount Factor: Do well-informed investors only buy efficient portfolios? |
I'm trying to implement the Hayashi - Yoshida estimator for correlation and there's something I'm missing with respect to realized correlation and realized variance. Assuming that $Y = \log P$, and that I have access to $N$ discrete (asynchronous) observations for two assets on a time grid $[0,t]$, the HY estimator is ... |
I'm looking at EUR/USD fwd prices. Currently they are the following ones:
[![enter image description here][1]][1]
These are the swap points to be added to the spot price. It seems it increases with time. Therefore, since overnight value date falls before spot value date, I'd expect ON swap points to be negative, ... |
Why is overnight more expensive than spot in an increasing forward swap values table? |
I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: *On covariance estimation of non-synchronously observed diffusion processes*, 2005) and there's something I'm missing with respect to realized correlation and realized variance. Assuming that $Y = \log P$, and that I have a... |
How can we expand this sum? $\sum_{i=1}^n (e^{rt_i-\frac{1}{2}\sigma^2t_i+\sigma w_{t_i}})^2$ where: $w_{t_i}$ is a standard Brownian motion.
If we let $m_t=e^{-\frac{1}{2}\sigma^2t_i+\sigma w_{t_i}}$ is a martingale where $m_0$ = 1, why does it reduce to $\sum_{i,j=1}^n e^{r(t_i+t_j)+\sigma^2\;min(t_i, t_j)}$.
I... |
Why not using a volatility indicator if volatility is the only factor? set 2 thresholds and you are done.
Separately recommend the read of a time series analysis or econometrics book, which will provide you with a deeper answer. |
Why not using a volatility indicator if volatility is the only factor? set 2 thresholds and you are done.
Separately recommend the read of a time series analysis or econometrics book, which will provide you with a deeper understanding. |
Suppose Id like to have 10 % of much portfolio allocated to "long volatility" either by rolling straddles or buy x % monthly OTM options when market is up or down y %.
Obviously going all in on one trade implies significant risk of loosing all the money. Does anyone know how one could structure such a strategy i.e s... |
Suppose I'd like to have 10 % of my portfolio allocated to "long volatility" either by rolling straddles or buy x % monthly OTM options when market is up or down y %.
Obviously going all in on one trade implies significant risk of losing all the money. Does anyone know how one could structure such a strategy i.e som... |
**Question:** I currently graduated with a Bachelor's in mathematics. I have taken classes in analysis up to and including introduction to measure and integration theory, probability theory without measure theory, point-set topology, complex analysis, pdes, and introductory abstract algebra, as well as an intro to math... |
What is the best way to model implied volatility surface in filtered historical simulation (other than keeping it constant)? Is it appropriate to apply GARCH-like model to every point on the surface? Any reduction techniques? Any suggestions will be appreciated.
Thanks. |
(I'm not in finance, so pardon my ignorance)
In The Big Short (2015), there is a little story about [Cornwall Capital][1]'s early trading strategy:
> Their strategy was simple and brilliant. Jamie and Charlie found markets will sell options very cheaply on things they think will never happen. So when they were wr... |
Why would the market systematically underestimate the probability of unlikely events? |
(I'm not in finance, so pardon my ignorance)
In The Big Short (2015), there is a little story about [Cornwall Capital][1]'s early trading strategy:
> Their strategy was simple and brilliant. Jamie and Charlie found markets will sell options very cheaply on things they think will never happen. So when they were wr... |
If Bank A buys 10mm of a 30 delta call from Bank B, then sells 3mm of the forward to Bank B as a delta hedge, then you can think of the 3mm delta hedge as (short 3mm call plus long 3mm put) using put call parity. Therefore , the overall trade can be thought of as : bank A buys 7mm of a call and 3mm of a put at the sa... |
I am trying to write a Python function that performs some calculations using a list of Quantlib options, and I would like to pass only that list without other information. In particular, the strike of each option is embedded there somewhere, but I am finding it hard to extract. Here is a toy example of an instance (ext... |
How can I extract the strike price from a Quantlib option object? |
Suppose I'd like to have 10 % of my portfolio allocated to "long volatility" either by rolling straddles or buy x % monthly OTM options when market is up or down y %.
Obviously going all in on one trade implies significant risk of losing all the money. Does anyone know how one could structure such a strategy i.e som... |
So from my understanding Hull (2012) f.e. shows that the optimal hedge ratio minimizes the variance of the returns. But what happens to the variance of the prices? Is the Minimum variance hedge portfolio also the one, which has the lowest variance at the price level? For example, if I compute the optimal hedge ratio fo... |
I set up a simple problem
Payment after .4 year is 25. The rate is 10%. I calculated PV as 25/(1+10%)^.4 = 24.77
Then I did Rate(.4,25,-24.77,0), and Rate function did not return any value. Can anyone explain why? |
I set up a simple problem
Payment after 0.4 year is 25. The rate is 10%. I calculated PV as $\frac{25}{(1+10\%)^{0.4}} = 24.77$
Then I did `Rate(0.4,25,-24.77,0)` in Excel, and `Rate` function did not return any value.
Can anyone explain why? |
Suppose I'd like to have 10 % of my portfolio allocated to "long volatility" by rolling straddles .
Obviously going all in on one trade implies significant risk of losing all the money. Does anyone know how one could structure such a strategy i.e some kind of simple way to keep a decent amount of capital over time, ... |
Consider the Cox Rubinstein binomial pricing model with N steps, with stock price change given by parameters u and d so that at step $i$ we have $S_{i+1} = uS_{i}$ or $S_{i+1} = dS_{i}$ with $0\leq i \leq N$. Let $r$ be the risk free rate. As usual suppose we have a cash instrument growing at the risk free rate, and as... |
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