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0
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1answer
42 views

Ho-Lee model - A and B derivation for $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$

I am analyzing the transition of the bond prices in the affine models in the form of $P(t,T)=e^{-A(t,T)-B(t,T)r_t}$ using the property that the diffusion and the drift of an affine model can be ...
7
votes
1answer
136 views

How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks? I suppose to form a baseline it would have to be ...
1
vote
1answer
44 views

Vasicek model problem

I am analyzing a problem where the below is given Vasicek model with risk-neutral dynamics $$dr_t = \kappa (\theta - r_t)dt + \sqrt{r_t} dW_t \quad \quad (1) $$ bond prices ...
0
votes
1answer
32 views

SABR Calibration: Normal vs Log-Normal Market Data

This question is about getting some clarification as to how to understand market quotes for normal & log-normal vols together with certain model assumptions. So let us define ...
5
votes
1answer
141 views

Extrapolating SVI

In his paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ $$ w(k) = a + b\{\rho (k-m) + \sqrt{(k-m)^2 + \sigma^2} \}.$$ Assuming that ...
0
votes
1answer
23 views

shifted SABR - ATM vol

quick question guys. I know that for Shifted SABR (or any other Shifted model), we simply model the underlying price process (lets say the forward interest rate F), as F' = F + x, x being the shift. ...
1
vote
1answer
81 views

2 Ito processes - $d(X_{t} + X^{'}_{t})^2 = (Y_t + Y^{'}_{t})^2 dt$ why it is true?

Having two Ito processes $dX_{t} =z_{1} dt + Y_{t} dB_t $ $dX^{'}_{t} =z^{'}_{1} dt + Y^{'}_{t} dB_t $ I am analyzing a proof of the product rule $d(X_t X_t^{'})=X_t dX_t^{'}+ X_t^{'} dX_t + ...
6
votes
2answers
2k views

Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
2
votes
0answers
24 views

Heston Model Maximum Return Distribution

What is the joint probability distribution of the maximum of the return between time $0$ and $t$ and the return at $t$, for the Heston model, when the return drift is $0$ and the correlation between ...
4
votes
1answer
79 views

Realized variance in SVJJ (Heston with jumps) model

I am working with the stochastic volatility model with jumps in both the price and volatility dynamics, ie. the risk neutral dynamics are of the form: $\mathrm{d}V_t = \kappa(\theta - V_t)\mathrm{d}t ...
4
votes
1answer
73 views

A question on implied volatility surface

Let a stock price process be $(S_t)_{t\geq 0}$ and let $(K, T)\longrightarrow \sigma^*(K,T)$ be the volatility surface corresponding to vanilla options on the stock. What is, for any time $T$ the ...
4
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0answers
34 views

delta hedging with stochastic volatility

In my thesis I want to work with delta hedging with stochastic volatility using Black-Scholes model. How will you suggest I implement numerical solutions using data from the real world? Beside Monte ...
1
vote
0answers
63 views

School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
0
votes
0answers
24 views

wishart stochastic volatility models

Stochastic volatility models assume that volatility follow a random process.In the emerging market the volatility tend to be high. why is it that the wishart stochastic volatility model fit well the ...
1
vote
2answers
53 views

Martingale correction for Andersen scheme with Interest Rate

I have implemented martingale correction to my Andersen scheme for Heston model, as it is in the paper (page 19-22): ...
1
vote
0answers
91 views

Heston model - Andersen scheme implementation

I would like to implement Andersen scheme for Heston simulation. On the following snipped is my code for generating asset path: ...
8
votes
3answers
316 views

Why is there a stong intraday-correlation between spot and vol?

Fig.1 shows an intraday scatterplot of the DAX future against its volatility index VDAX on 6-Jan-2016. The data suggest a strong negative correlation between the two. There are various models ...
1
vote
2answers
74 views

Where to find pricing formulas for affine stochastic volatility jump-diffusion models?

Does anyone know a reference where I can find the pricing formulas for vanilla calls in the affine stochastic volatility jump diffusion class of models such as SVJ and SVJJ? I am looking for ...
0
votes
1answer
41 views

Motivation: Stochastic Interest rate model

what is a reason that someone might be interested in a stochastic-interest model such as the Chen model? Also can you provide me with a link to an easy to read motivational paper/part of a paper on ...
2
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0answers
44 views

When to use SV or a GARCH model

So i have been searching for this answer for a question if there is a rule or something that would say when to use GARCH type model or use an stochastic volatility model to predict the volatility of ...
1
vote
1answer
69 views

Implied volatility as price transform

Implied volatility The way I understand it, traders often think of implied volatility as a transformed price. So in a way, the Black Scholes model is considered a 'model-free' blackbox that takes a ...
2
votes
2answers
104 views

Calibrating stochastic volatility model from price history (not option prices)

For stochastic volatility models like Heston, it seems like the standard approach is to calibrate the models from option prices. This seems a bit like a chicken and an egg problem -- wouldn't we ...
2
votes
1answer
542 views

Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
3
votes
1answer
300 views

Stochastic Volatility CIR estimation

Would anyone have a code (pref. Matlab or R) for any type of estimation (QML, GMM) not using option prices of a stochastic volatility model driven by a CIR process described below? \begin{equation} ...
1
vote
1answer
35 views

SVI calibration, why fit to option prices and not implied volatilities

Bear with me. Related (very good) question: How to calibrate a volatility surface using SVI From this paper http://arxiv.org/pdf/1204.0646.pdf, page 21. Why does the recipe suggest fitting to option ...
1
vote
1answer
53 views

Applying interest rate models for volaility rate

To what extent may the interest rate models be applied for modeling implied volatity? The story: I was checking different stochastic option pricing models for being able to replicate implied ...
5
votes
0answers
111 views

Why is it useless to model stochastic volatility when pricing Vanilla style derivatives?

With respect to the answer by user AFK in Ideas about Stochastic volatility models. I am specifically interested in interest rate options (IR Caps/Floors and Swaptions).
5
votes
1answer
166 views

Filtering out AR(1) effects before using stochastic volatility model

I wonder if I first filter out AR(1) (autoregressive model with lag 1) effects from univariate time series and then fit stochastic volatility model does above procedure introduce any bias at first or ...
0
votes
0answers
62 views

Practical Delta hedging under stochastic volatility models (e.g. SABR model)

I'm currently straggling with Delta hedging under SABR model (or other stochastic volatility models). As far as I know there are numerous Delta hedging strategies theoretically and practically such as ...
3
votes
0answers
75 views

Approximate asian geometric option with Heston

I am trying to implement Theorem 1 from this Journal in RStudio. The journal says the it is possible to find a approximate price of a geometric asian option in a Heston setup this way: ...
0
votes
3answers
101 views

Why Jumps in Option Pricing models?

The Bates model adds a Jump process to the Underlying. I understand this may represent observed time series more realistically, but why would one care about this in option pricing? The option price ...
4
votes
1answer
203 views

Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility

I am looking to measure the volatility from the open of the market until a trade takes place and use that volatility in post-trade regressions to help explain transaction costs. A simple regression ...
3
votes
1answer
389 views

Option prices in Bates SVJ model?

In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model. There exists an important extension of Heston model to include diffusion jumps, known ...
5
votes
1answer
124 views

Market price of volatility risk

Reading Gatheral's The volatility surface, page 7. The model they are talking about is ...
3
votes
1answer
210 views

Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
1
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0answers
142 views

Reference request about stochastic volatility model

I'm fiddling with estimation of stochastic volatility models and have build up a somewhat flexible framework using indirect inference. I would like to try and throw a lot of different continuous ...
2
votes
1answer
112 views

How to use calibrated Standard Stochastic Volatility?

I'm considering the standard stochastic volatility model: $$x_t = \rho x_{t-1} + \sigma \epsilon_x$$ $$y_t = \beta \exp\left[ \frac{x_t}{2} \right] \epsilon_y$$ where $y_t$ is the log-returns and ...
0
votes
1answer
99 views

A Difference between Local Vol and Stochastic Vol Models

For the purpose of this question a local vol model is a 1d SDE which specifies the price process and we have a contingent claim that depends on those prices (in general, at multiple times). e.g. ...
1
vote
1answer
116 views

Validation of Bates SVJ model

I have just finished implementing the Bates model for pricing European call options. To check results, I have been looking for a validation set where I could see the Bates parameter values and ...
6
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0answers
90 views

Transition densities in the Heson model

Knowing the Characteristic function $\Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t]$ (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ...
1
vote
2answers
93 views

Garch for covariance matrix?

I have seen plenty of literature about GARCH on estimation volatility. how about covariance? There are plenty of risk models depending on the covariance matrix. I guess we can assume the correlation ...
2
votes
1answer
452 views

using garch to forecast volatility but getting low persistence model

I am using a GARCH(1, 1) model to try model volatility for a certain stock. I have a GARCH function in matlab that returns the three parameters, omega, alpha & beta. I then use this parameters ...
3
votes
1answer
528 views

Covariance matrix and Cholesky decomposition

I am simulating a spread option with stochastic volatility using Monte Carlo simulation. I have the positive-definite covariance matrix $$ \rho = \left( \begin{array}{cccc} 1 & \rho_{1,2} & ...
1
vote
2answers
218 views

Option Prices under the Heston Stochastic Volatility Model

I was wondering if anyone has come across a more straightforward derivation of the semi-closed form solution for the price of a european call under the Heston model than the one proposed by Heston ...
2
votes
1answer
141 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
1
vote
1answer
156 views

derivation of heston pde in gatheral

Following Gather (the volatility surface, chapter 2) we assume the following process: $$ dS_t = S_t(\mu_t dt+\sqrt{\nu_t}dZ^1_t)$$ $$ d\nu_t= -\lambda(\nu_t-\bar{\nu})dt+\eta\sqrt{\nu_t}dZ^2_t$$ ...
4
votes
1answer
314 views

Quadratic exponential method (by Andersen) in Heston model

I am having trouble understanding the reasons that led Andersen to define his QE scheme to efficiently simulate Heston Stochastic volatility model (you may check the celebrated scheme here). The ...
2
votes
1answer
137 views

Do we need Feller condition if volatility process jumps?

It is fairly known that in affine processes, as Heston model \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{v_t} S_t dW^{S}_{t} \\ dv_t &= k(\theta - v_t) dt + \xi \sqrt{v_t} ...
4
votes
2answers
179 views

arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy \begin{equation} dB_t = B_t r dt \end{equation} \begin{equation} \quad \quad \quad \quad \, ...
6
votes
2answers
294 views

Does it make sense to use upward and downward volatility in option pricing?

Historically stocks have a higher likelihood to increase in price than to fall in price. As such would it make sense to split a stocks volatility measurement into upward and downward components? For ...