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You missed to mention a lot of details in your link.
- Firstly, the XCCY Swap is said to be an approximation of an FX forward and swaps, not just swaps.
- Secondly, the FX swap is approximated.
- Thirdly, the swaps are approximated, assuming a flat yield curve (which is never the case).
- It is for approximating... |
Under the Black-Scholes framework, is there any approximation of option delta (i.e., $N(d_1)$) or binary options price(i.e., $N(d_2)$) given the option price $C$?
Of course, you can calculate those once you know the implied volatility (IV). I am looking for an approximation __without__ using IV. A very rough approxim... |
Rough approximation of option delta (or binary option) given option price wihtout implied volatility? |
I am looking for a qualitative assessment regarding the (negotiable) 'cost' incurred when two counterparties agree on collateralizing existing derivatives business. I think the core of my question is:
What is the admissible / theoretically justifiable 'negotiation space' when it comes to (trying to) charging fees f... |
What is the expectation of Bt^4 and Bt^3 given Bs? Given t>s.
I understand that the expectation of Bt given Bs is Bs and that the expectation of Bt^2 given Bs is something like Bs - s + t.
|
What means segregated margin call and non-segregated margin call in the example. Why it is calculated that way？ Thank you.
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.isda.org/a/zR2gE/Margin-Approaches-New-Edited-August-2022.pdf&ved=2ahUKEwjt25qj3u77AhU9s1YBHdvCARsQFnoECDwQAQ&usg=AOvVaw1NEaztnWa... |
I got following code from the [Quantopian Lecture](https://www.youtube.com/watch?v=Yp7oJgY82cY) about factor investing. Following is calculating momentum factor. Earlier in the lecture, instructor told that, we will sort the securities based on their factor score and go long on top quantile and short on bottom quantile... |
How momentum factor is calculated? |
Below are some of the sources one can use to search for and view or download research articles and other publications on quantitative finance (QF). Many include non-peer-reviewed articles in their search results. Most carry or index articles in languages other than English.
The list of sources for any category is n... |
is it correct to say that floating rate notes (FRNs) have no roll-down for a time horizon as it is interest risk free? |
Despite **risk**-factor models like [Fama/French
(1993)][1] or q-theory based models like [Hou et al. (2015)][2], others have proposed factor-models to capture **mispricing** in equities, e.g. [Stambaugh/Yuan (2017)][3] and [Daniel et al. (2020)][4]. Even for non-equity markets, risk-models are developed like most rec... |
I am doing some self study on stochastic local volatility modelling and am having a hard time replicating some results from [this paper](https://faculty.fordham.edu/rchen/Fenics.pdf). The paper provides the data used to extract the discrete implied vol. surface which I managed to successfully replicate. My struggle is ... |
I am doing some self study on stochastic local volatility modelling and am having a hard time replicating some results from the paper "[FX Option Pricing with Stochastic-Local Volatility Model](https://faculty.fordham.edu/rchen/Fenics.pdf)" by Zhu et al (2014).
The paper provides the data used to extract the discre... |
John Hull mentioned in his book using Cash Price(Dirty Price) instead of Quoted Price(Clean Price) in pricing a bond option using Black-Scholes. If confuses me as it seems more natural to assume the return of bond price stripped of accrued interest follows a Geometric Brownian Motion. Accrued interest ifself does not h... |
John Hull mentioned in his book using Cash Price(Dirty Price) instead of Quoted Price(Clean Price) in pricing a bond option using Black-Scholes. It confuses me as it seems more natural to assume the return of bond price stripped of accrued interest follows a Geometric Brownian Motion. Accrued interest ifself does not h... |
A lot has been written about the fact that the expected return of the underlying asset is not part of the Black Scholes formula. I understand the argument that the performance of the underlying asset can be hedged out via delta hedging and that the dealer who has sold the option is therefore indifferent to the performa... |
No expected return in Black Scholes formula: But how about the gamma? |
I am trying compute a variance/covariance matrix for 5 stocks using monthly returns. I plan to use CAPM (using monthly log returns) as the expected return and the US 3-month Treasury Bill (UST3M) monthly return as the risk free return in the variance/covariance formula, yielding the excess returns. How should I compute... |
## Theory: ##
Based on [Hansen/Jagannathan][1], the set of means and variances of returns is limited. With $R^f$ as the risk-free rate, $R_i^e$ as the return of stock $i$ in excess of $R^f$ and a stochastic discount factor $m$, we know:
$$\frac{\sigma(m)}{\mathrm{E(m)}} \geq \frac{\lvert \mathrm{E}(R_i^e)-R^f \rv... |
I have different large datasets consisting of 1000 stocks each. I want run a FF3 regression
I regress my monthly returns (minus riskfree rate) of the dataset against the Mkt-RF, SMB and HML factor.
But as alpha I always receive a value which is close to zero (0.001)
For Beta1 (MKT-RF) I receive 1.08
Beta2 (SM... |
I have two questions about the CAPM model: the first is theoretical while the second is related to observed market data.
**First question**:
let's say we have company A and company B and we want to estimate their expected returns within the CAPM model.
In this model the percentage of systematic risk is given b... |
1. If the two companies have indeed the same beta, then company A will have more total risk. Or in other words company A has more idiosyncratic risk (i.e. the risk that is not explained by the model);
2. If the historical average return is 60% (is this yearly?) and the CAPM implies an expected return of 11% for th... |
I investigate a specific case of a funded equity collar. Let s assume that counterparty A has already a stake in a share XYZ and wants to get funding out of it from a bank B which does not want to get too much credit exposure. If I refer to the theory, the bank B can offer a margin loan to counterparty A which must pl... |
How to apply a funded equity collar to illiquid stocks? |
I am trying to run a Quantlib Python Monte Carlo simulation using either the ql.BlackScholesMertonProcess or the ql.GeneralizedBlackScholesProcess. I have a vol surface that I have generated using ql.BlackVarianceSurface. I am using ql.GaussianMultiPathGenerator as my path generator.
I would like the Monte Carlo p... |
I investigate a specific case of the funded **equity collar** [[1]].
Let's assume that counterparty $A$ already has a stake in share $XYZ$ and wants to get funding out of it from a bank $B$, which does not want to get too much credit exposure from the resulting operation.
If I refer to this question [[1]], bank $... |
Reference paper: [Dealing with the Inventory Risk (Lehalle, Gueant, Tapia)](https://arxiv.org/abs/1105.3115)
∆T is the time horizon over which you compute the intensities of aggressive orders (you get the k and A parameters)
I have two questions:
1) The choice of ∆T is not discussed in detail. How can we determi... |
I've tried to build a basic one-factor Hull-White model using python, which I've done by trying to discretise the characteristic SDE.
According to my notes, the Hull-White SDE is
$$
dr_t = \alpha (\mu(t) - r_t) dt + \sigma dW_t
$$
where $\alpha$ is a parameter determining the rate of mean-reversion, $\mu(t)$... |
Is this the correct discretisation of the Hull-White SDE for building a python model? |
I understand this is very basic question but I still scramble to determine what would be right risk free rate to price a simple European call option using Black-scholes formula, with maturity is 5 years. This option is written on a USD based stock?
I have below choices
1. US Treasury rate with maturity 5 years (... |
What exactly is the settlement date for a forward starting swap trade ?
Say today is 13rd Dec 2022, is the settlement date of 1 year forward starting swap 13rd Dec 2023 or 15th Dec 2023 ?
i.e., Is the settlement day offset (2 days) taken into account for forward starting swaps? |
Say today is 13rd Dec 2022,
For a spot staring swap, its settlement date would be 15th Dec 2022 assuming the settlment offset is 2 days.
What is the settlement date for a one year forward starting swap trade ?
is the settlement date 13rd Dec 2023 or 15th Dec 2023 ?
|
I've tried to build a basic one-factor Hull-White model using python, which I've done by trying to discretise the characteristic SDE.
According to my notes, the Hull-White SDE is
$$
dr_t = \alpha (\mu(t) - r_t) dt + \sigma dW_t
$$
where $\alpha$ is a parameter determining the rate of mean-reversion, $\mu(t)$... |
As long as you price on the outright forward and not on forward points (which is how most forwards are quoted in the market), this is essentially the same coin, looked at from different sides. If you had an option on points, you would ideally need a hybrid model for FX and IR to take into account stochastic interest ra... |
I'm reading a paper that says:
> We remark that negative R^2 values do not imply that the forecasts are economically meaningless. To emphasize this point, we will incorporate these return forecasts into two common forecast-based trading strategies, and showcase their profitability...
The authors proceed to do just ... |
Model is economically significant, but has negative r^2? |
I'm reading a paper by Rama Cont that [says][1] (Page 25):
> We remark that negative R^2 values do not imply that the forecasts are economically meaningless. To emphasize this point, we will incorporate these return forecasts into two common forecast-based trading strategies, and showcase their profitability...
The... |
## Theory: ##
Based on [Hansen/Jagannathan][1], the set of means and variances of returns is limited. With $R^f$ as the risk-free rate, $R_i^e$ as the return of stock $i$ in excess of $R^f$ and a stochastic discount factor $m$, we know:
$$\frac{\sigma(m)}{\mathrm{E(m)}} \geq \frac{\lvert \mathrm{E}(R_i^e)-R^f \rv... |
I had a doubt when going across the ways in which a trade happens. I have read that fora trade to happen, the buy order's price (bid) must match the sell order's price (ask). Now, what happens, if they are off by say 1/100th of a dollar. Will the trade still not happen? If it does, at what price will it trade? |
For a trade to occur, should the ask price EXACTLY match the bid price, down to the last decimal point? |
After thinking about this problem more, I believe I understand what drives this behavior of a negative R^2 and positive PnL. Suppose that you are trading a long-short portfolio (as in the paper), and your out-of-sample data has an unconditional mean that is very different from your in-sample. But, suppose your foreca... |
Is there any specific name for the spread between US Treasury vs OIS rate?
I observed that for a specific tenor (e.g. 10 years) US Treasury is higher than the OIS curve. Any reason for this? OIS is unsecured so should not OIS be higher than Treasury rate which is backed by US Govt hence less credit risk? |
The current UK Rate is 3.5. However, SONIO index is at 3.4269.
What is the reason for SONIO Index being lower than UK Rates?
|
Why is SONIO Index is lower than UK Rates? |
### It is a consequence of (direct) proportionality from equation (2.10):
Equation (2.10) states that the change in price ($\Delta p)$ is proportional to the logarithm of the market order size $Q$:
$$
\Delta p \propto \ln(Q).
$$
From the definition of **[direct proportionality](https://en.wikipedia.org/wiki... |
Having done FX trading as a hobby for nearly two years now (and having made some profit overall), I now have got a fundamental question which I *think* I already have the answer to, but I would like to know for sure.
My question is if the risk for long positions is higher than for short positions or vice versa in FX... |
Why is SONIO Index lower than UK Rates? |
Coming rather late to this party and because I've been researching the same (or at least similar) question, I'd like to share my solution:
I've signed up (for free) at [lemon.markets][1] to request an API key. Following [their documentation][2] you can use the REST API to e.g. query for a certain ISIN with the lates... |
Coming rather late to this party and because I've been researching the same (or at least similar) question, I'd like to share my solutions:
### First provider
I've signed up (for free) at [lemon.markets][1] to request an API key. Following [their documentation][2] you can use the REST API to e.g. query for a cert... |
I am reading Bergomi's book Stochastic Volatility Modelling. In the chapter 6 dedicated to the Heston model, page 202, he describes the traditional approach to first generation stochastic volatility models :
1. You start with historical dynamics for the instantaneous variance : $$dV_t = \mu(t,S_t,V_t,p)dt + \alpha ... |
Why is the market price a risk a non-entity according to Bergomi? |
I am reading Bergomi's book Stochastic Volatility Modelling. In the chapter 6 dedicated to the Heston model, page 202, he describes the traditional approach to first generation stochastic volatility models :
1. You start with historical dynamics for the instantaneous variance : $$dV_t = \mu(t,S_t,V_t,p)dt + \alpha ... |
Why is the market price of risk a non-entity according to Bergomi? |
Cool question!
In the following, I first use the fact that cosine of $\frac{\pi}{2}i$ is zero for odd numbers. I then rewrite $\cos(\pi i)$ as $(-1)^i$. Then, I add the zeroth term, apply the well-known formula for an alternating geometric series
(Taylor series of $\frac{1}{1+x}$) and simplify:
\begin{align*}... |
What is the best volatility model to price Down-In Puts (DIP) under several stress scenarios (e.g downward movement of underlying price by -5%, -10%, -15%)?
Please note that I got the market prices for all vanilla put options on the underlying assets and I have calculated the implied volatilities. Also, I use the fo... |
I am reading Bergomi's book Stochastic Volatility Modelling. In the chapter 6 dedicated to the Heston model, page 202, he describes the traditional approach to first generation stochastic volatility models :
1. You start with historical dynamics for the instantaneous variance : $$dV_t = \mu(t,S_t,V_t,p)dt + \alpha ... |
What is the closed-form solution for the PV of the following series? |
Suppose that I am placing a market order directly in the order book of an exchange. For market orders, it seems quite clear that larger orders obtain larger spreads due to the fact that - without loss of generality - a large market buy order must reach further into the limit sell orders of the order book than would a s... |
Suppose that I am placing a market order directly in the order book of an exchange. For market orders, it seems quite clear that larger orders obtain larger spreads due to the fact that - without loss of generality - a large market buy order must reach further into the limit sell orders of the order book than would a s... |
Is it possible to get hourly or minute-by-minute data (in the form of a dataframe) in Python using one of the API wrappers (```xbbg``` or ```pdblp```)? Using the former, ```blp.bdh``` and ```blp.bdip``` don't seem to work. The latter only gives bar data, which I understand isn't available for more than 140 days. |
Asset pricing uses the concept of a stochastic discount factor (SDF). I have read various things about it but have not seen a concrete example. Could you give a concrete example of an SDF, e.g. one that has been estimated in an academic paper or being used by practitioners? |
Asset pricing uses the concept of a stochastic discount factor (SDF). I have read various things about it but have not seen a concrete example. Could you give a concrete example of an SDF, e.g. one that has been estimated in an academic paper or being used by practitioners? (E.g. could it be F-distributed? Lognormally ... |
what does a negative and a positive intercept imply in spanning regression or factor redundancy test? For example, value factor is regressed on the mkt, smb, rmw, and cma and the intercept is negative and insignificant. What will be the interpretation of this intercept in connection with the set of other factors? |
What is the trade description behind a call option on a forward? How can it be described with words and not with mathematical formulas?
So what is the intuition behind the following payoff:
$$Payoff_{1}=\max\left(F\left(T,\tilde{T}\right)-K,0\right)$$
and how does it differ from the following payoff:
$$Payo... |
I feel I am fundamentally misunderstanding something when it comes to futures on options. On the bottom of page 98 of 2nd edition *Option volatility and Pricing* by Natenberg he says:
"*In the US, options on futures are subject to stock-type settlement, while outside the US, options on futures are usually subject to... |
Why does Natenberg say that when future options with future-type settlement are traded, no money changes hands? |
I do not think such an upper bound exists for beta in terms of moments of the SDF alone. The upper bound of beta depends on the volatility of the SDF and the volatility of the asset returns. The former is given from its factor mimicking portfolio, the latter can be arbitrarily large.
## Sharpe ratios
To start wit... |
I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such derivatives in practice. How do banks manage their interest rate caps and floors books?
The easiest approach seems to be del... |
How do sell-side institutions manage interest rate derivatives books in practice? |
I feel I am fundamentally misunderstanding something when it comes to options on futures. On the bottom of page 98 of 2nd edition *Option volatility and Pricing* by Natenberg he says:
"*In the US, options on futures are subject to stock-type settlement, while outside the US, options on futures are usually subject to... |
I understand the finance 101 explanation of how to minimize variance of a long-short portfolio using a covariance matrix. I also know that it doesn't really work because the covariance matrix is unstable out of sample. It has been suggested that in practice factor risks are more stable out of sample, but I don't quite ... |
This will NOT work.
You cannot get `ICVS` curves in API. Excel has a curves toolkit for excel. However, for `WAPI`, you need enterprise licenses (not part of terminal subscription). Your account manager can help you with that if that is truly needed.
What you do here, is simply a FLDS field. Check out `YCSW0045 ... |
I have the european volatility surface of a given asset. What is the correct procedure to compute the price of the options with american exercise type? |
How can I derive the price of american options given the european options prices? |
John Hull mentioned in his book using Cash Price(Dirty Price) instead of Quoted Price(Clean Price) in pricing a bond option using Black-Scholes. It confuses me as it seems more natural to assume the return of bond price stripped off accrued interest follows a Geometric Brownian Motion. Accrued interest itself does not ... |
This may sound like a basic question but I have seen many large institutional investors have this as part of their asset allocation and am wondering why they do this?
Does it make sense to have a large allocation to short term funds (such as repo and other short term fixed income instruments); and simultaneously hav... |
Does it make sense to have an allocation to short term fixed income and a leveraged or unfunded position? |
I'm trying to program a basic forex simulator in order to test strategies. But I don't know how is influenced the market when a position is opened or closed.
For example, if I open a 10 000 000 € BUY order on EURUSD, I think It will decrease the quote of the EURUSD value. But maybe I'm wrong, and I don't know how mu... |
How a trade influence the forex market? |
I'm trying to program a basic forex simulator in order to test strategies. But I don't know how is influenced the market when a position is opened or closed.
For example, if I open a 10 000 000 € BUY order on EURUSD, I think It will decrease the quote of the EURUSD value. But maybe I'm wrong, and I don't know how mu... |
Looking at [Opdyke, J.D., Comparing Sharpe Ratios: So Where are the P-Values?][1], page 22 (Appendix A) an application is given for the Propagation of Errors formula on a ratio of two random variables:
$$\operatorname{Var} (x_1/x_2)=\left[ \frac{E[x_1]}{E[x_2]}\right]^2\left[\frac{Var(x_1)}{E[x_1]^2} + \frac{Var(x_2... |
Looking at [Opdyke, J.D., Comparing Sharpe Ratios: So Where are the P-Values?][1], page 22 (Appendix A) an application is given for the Propagation of Errors formula on a ratio of two random variables:
$$\operatorname{Var} (x_1/x_2)=\left[ \frac{E[x_1]}{E[x_2]}\right]^2\left[\frac{Var(x_1)}{E[x_1]^2} + \frac{Var(x_2... |
The classical Markowitz objective is:
$$
f(w) = w^T \mu - \frac{\lambda}{2} w ^T \Sigma w = \mathbb{E}[r^Tw] - \frac{\lambda}{2} \sigma^2(r^Tw)
$$
where $\mu$ is the vector of mean returns. This is a quadratic function, and we can directly/analytically solve for the solution in the unconstrained case, as well as in... |
The Viability/Usefulness of Mean Standard Deviation Optimization? |
The classical Markowitz objective is:
$$
f(w) = w^T \mu - \frac{\lambda}{2} w ^T \Sigma w = \mathbb{E}[r^Tw] - \frac{\lambda}{2} \sigma^2(r^Tw)
$$
where $\mu$ is the vector of mean returns. This is a quadratic function, and we can directly/analytically solve for the solution in the unconstrained case, as well as in... |
Unless I am missing the obvious, I do not see the question being answered? In my opinion trying to understand in simple language what $\alpha, \beta, \rho$ mean requires an explanation what these parameters do and why it is useful.
Here is my attempt:
Black (all Black Scholes formulas) assume(s) that Implied Vol... |
**Short Version**
- Market standard is to use Normal Vol (used in the Normal / Bachelier model)
- Market data comes from contributors like Tullett, ICAP and the like and can be premium and vol quoted etc.
- Usually, these quotes are filtered and combined into a generic quote (e.g. BVOL for Bloomberg Volatility)
- ... |
**Short Version**
- Market standard is to use Normal Vol (used in the Normal / Bachelier model)
- Market data comes from contributors like Tullett, ICAP and the like and can be premium and vol quoted etc.
- Usually, these quotes are filtered and combined into a generic quote (e.g. BVOL for Bloomberg Volatility)
- ... |
Although this question was something new at the time of writing, it is probably clear now that plugging negative interest rates into Equity / Index options is no problem at all. The reason interest rate options (swaptions, caps, floors etc) switched to pricing with Bachelier (Normal) model is that the underlying itself... |
Nothing new to @Matt Wolf's answer but a few more details. Although this question was something new at the time of writing, it is probably clear now that plugging negative interest rates into Equity / Index options is no problem at all. The reason interest rate options (swaptions, caps, floors etc) switched to pricing ... |
I was told that there is an active `CDS` market for insurance from US sovereign default. I am looking for the historical data in time series on this `CDS` (premium).
Does `Bloomberg` offer such data. If it does, can you please tell me what is the name of scrip/function to use to get this `CDS` data from `Bloomberg`?... |
I was told that there is an active `CDS` market for insurance from US sovereign default (in terms of treasury bond). I am looking for the historical data in time series on this `CDS` (premium).
Does `Bloomberg` offer such data. If it does, can you please tell me what is the name of scrip/function to use to get this ... |
### Other than the binomial expansion, what is the relationship between $B$ and $w$?
As I understand correctly, there is no immediate relationship between the lag operator $B$ and the weights $w$. However, going from the fractional differencing operator, $(1-B)^d$ to $\hat{X}_t$ can be done as follows:
\begin{align... |
In Joel Greenblatt's Magic Formula why is the holding period one year? Why not rebalance the portfolio once each two years? Or three years? |
For vanilla options put-call parity
$$
C - P = F
$$
must hold. On the other hand, it can happen that puts can have different implied vols than calls, due to for example shorting restrictions, borrowing costs, or if the underlying is not traded.
My interpretation would be that a long call and short put must hav... |
My current understanding of the theory behind the convergence of options prices using trees is the following:
Suppose $S = (S_{t})_{0\leq t\leq T}$ is the underlying process and $g(S_{t}:0\leq t\leq T)$ is the option we want to evaluate. Then we want to construct trees $S^{N}$such that $S^{N} \Rightarrow S$ (Here $\... |
I am aware that there is an active `CDS` market for insurance from US sovereign default (in terms of treasury bond) as *Dimitri Vulis*
commented. I am looking for the historical data in time series on this `CDS` (premium).
I was trying to get historical `CDS` data from `Bloomberg` and found ticker `US CDS USD 5Y` ... |
I am aware that there is an active `CDS` market for insurance from US sovereign default (in terms of treasury bond) as *Dimitri Vulis*
commented. I am looking for the historical data in time series on this `CDS` (premium).
I was trying to get historical `CDS` data from `Bloomberg` and found ticker `US CDS USD 5Y` ... |
I recently came across an example which does a simple delta hedging experiment. Below are the details:
"**Market conditions**
Interest rates are at a 2% level --> r = 0.02
The underlying stock pays no dividend and follows a Geometric Brownian Motion (GBM) with µ = 10% and σ = 20%
The initial spot price is ... |
I recently came across an example which does a simple delta hedging experiment. Below are the details:
"**Market conditions**
Interest rates are at a 2% level --> r = 0.02
The underlying stock pays no dividend and follows a Geometric Brownian Motion (GBM) with µ = 10% and σ = 20%
The initial spot price is ... |
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