# All Questions

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108 views

### Pricing and hedging of vanilla options based on non-tradable underlying

Consider a non-tradable stock index $S$ which satisfies: $dS_t=\mu S_tdt+\sigma S_tdW_t$ and a risk-free asset $B$. I want to price an European Call option with the payoff $C_T=max(S_T-K,0)$. The ...
100 views

### Complete Financial Market: Integrability condition for Contingent Claims

Consider an arbitrage-free and complete financial market with underlying filtered probability space $(\Omega,\mathcal{F},\{\mathcal{F}_{t}\}_{t\,\in\,[0,T]},\mathbb{Q})$, where $T\in(0,\infty)$ is ...
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### Calculating volatility of inhomogeneous time series

I am reading an article by Zumbach and Müller whose name is Operators on Inhomogeneous Time Series. This is interesting in general, but my main goal is to learn a good and efficient method to ...
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### Algorithmic Trading Model Calculation and Stale Data

I'd like ask everyone a more concurrency programming but definitely quant-finance related question. How do you deal with staleness of data in market hours as quote ticks are streaming and your model ...
946 views

### Fitting Student t-distributions to log-returns

It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without ...
159 views

### Dividend Index Futures

My question is dealing with the proportionality between Dividend Index Futures prices and Index prices. Indeed, we in the past we used to do a simple regression between these variables and use the ...
248 views

### LSM American Option pricing with dividends

Under the Longstaff-Schwartz LSM method for an American call, how should I account for a continuous dividend paying stock? I assume that it'll needs to be accounted for when simulating the underlying ...
127 views

### Risk neutral measure in exponential levy model

Is there a method of finding a risk-neutral measure for assets driven by the levy process? I understand there is the esscher transform but I think it tends to transform the processes into ...
129 views

### Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
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### EUR/PLN and EUR/USD delta-term-vol surface quoting convension

does anyone know for sure what is the FX market convension to quote delta-term pairs for EUR/PLN, for EUR/USD. I know that for EUR/PLN it should be delta p.a forward, for EUR/USD it should be delta ...
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### Estimation of ranks of log-returns via copula

I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order to be ...
418 views

### Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
642 views

### VaR backtesting with overlapping time intervals

Of course the issue here is dependence: can it be removed or accounted for (in independence tests too, which of course would be troublesome)? There's a lot of literature on regression in this setting, ...
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### Is it more accurate to analyze returns on a calendar day basis than a trading day basis?

I'm rather new to the actual practice of this kind of analysis, but it just seems wrong to me to throw Mondays' returns in with the rest without accounting for the passage of time on the weekend when ...
532 views

### Pricing with collateral

I have been confused about many things concerning the princing of securities with collateral. We can prove that today's price of a security( fully collateralized and within the same currency) is the ...
153 views

### Are there canonical test cases for testing of pricing engines

Short intro: We are developing pricing engines for the calculation of market risk in a Solvency II solution, including bonds, callable bonds, cds, options, futures and so on. Are there any canonical ...
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### Hasbrouck's information share

Given a cointegrated set of price series, I am trying to compute the Hasbrouck's information share, as described in page 12-13 of this article. page 7-8 of this article I have the vector error ...
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### Use of Local Times in Option Pricing

I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
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### Benefits of Diversification and Rebalancing with negatively skewed leptokurtic return distribution?

I am missing tools to investigate this issue. I am trying to solve this question here. What kind of issues should you acknowledge over the naive diversification/rebalancing with normal distribution? ...
1k views

### How to compute the realised intraday volatility?

I'm in the position to calculate a non-parametric volatility estimator for 15 and 30 minutes intervals of the SPY. I got data sampled on second resolution. However, I checked plenty of papers but, as ...
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### What type of interpolation should be used in key rate perturbation models?

When perturbing a key rate in order to assess sensitivity of portfolio value, what sort of interpolation is standard? A book I am looking at says linear, but this seems pretty unrealistic to me--and ...
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### Commerical delayed stock quote feed that is redistributable?

I'm looking for a commercial delayed quote feed that will allow us to distribute delayed US stock market quotes to the public (ie. that will allow us to display US delayed quotes on the Internet). We ...
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### Why does VIX need to calculate the Forward term?

From the reference, the Vix Whitepaper of CBOE, I found the formula of VIX. There are two terms. The first one is focusing on the info from Option contracts. And the second one is focusing on the ...
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### Anyone know if this daily report discontinue to publish? Goldman Sachs - “Global Index Volatility and Correlation Monitor”

I used to receive this daily report in my workplace from Goldman Sachs mailing list but the mailing list discontinued in May 2019 without any notice. The report is an pdf attachment which send from "...
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### Replication of a dividend swap

I wanted to know how banks replicate dividend swap, my best guess is to take the spread between a Total Return Swap and a Forward.
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### Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
109 views

### How to price the american options using local volatility

I have given with a surface of american option prices $C_{am}(T, K)$. From these american option prices the implied volatility surface is deduced. Now I want to find the local volatility $\sigma(s,t)$...
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### Why are thousand-ish-factor vendor risk models not extremely overfit and inaccurate?

Many vendor risk models have many hundreds, or even thousands of factors (many of which are highly correlated with each other). Underlying all these risk models is some sort of covariance matrix in ...
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### Is there an arbitrage free option model that treats volatility as a deterministic function of strike?

I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
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### Estimation of Radon–Nikodym derivative from hisotrical returns and option price data

Say we have an estimate of empirical density function $f^{\mathbb{P}}_S(s)$ of historical log-returns on a stock $S$ over a 30-day period under the real-world objective measure $\mathbb{P}$. We also ...
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### Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
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### American put option. Exercise time is a random variable, calculation of expected payoff

I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
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### Feynman-Kac to derive stochastic representation

$u_t + \frac{1}{2}\sigma^2x^2u_{xx} - \alpha + \lambda((K_d - x)^+ - u) = 0$ with terminal condition $u(T, X) = (K_m - X(T))^+$ $dX = \sigma X(t)dW_t$ $\alpha$ and $\lambda$ are constants Ok so ...
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### Strategy for implied volatility

I encountered this question: "A trader observed that the implied vol of OTM calls and puts are higher than that of ATM option, what is the best strategy among: Calendar Spread, Bull Spread, Bear ...
The solution of the model contains constant: $k = \alpha K$, it relates to: (i) probability of getting a fill ($\alpha$) and (ii) market impact ($K$). Estimating (i). The author proposes that the ...