Questions tagged [stochastic-volatility]

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Bates Model Jump Percentage Parameters

I am trying to calculate the jump parameters for the Bates volatility jumps, specifically, the mean of the jump percentages, $\mu_j$. For the value of $J$, I am using jumps $|\frac{s_{i}-s_{i-1}}{s_{i-...
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1answer
464 views

Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \begin{equation} \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} \end{...
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1answer
79 views

Compute implied volatility surface of a put option from a call option

Suppose the function double bsCall(double S0, const double &K, double T, double r, double sigma) computes analytically the Black-Scholes price of a call option ...
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1answer
132 views

Rough Volatility Prediction - Gatheral, Jaisson, Rosenbaum Paper

I just read through the paper "Volatility Is Rough" by Gatheral, Jaisson and Rosenbaum. There is a website (link: http://tpq.io/p/rough_volatility_with_python.html) that details the simulations they ...
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53 views

Finding Jump Probability For Time Series Data

I'm relatively new here, so if it seems like I'm asking a bad question, go easy on me. So I was looking at the Merton Jump Diffusion Stochastic Model on Turing Finance's article. Instead of creating ...
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1answer
106 views

Are extended SABR models useful for options with non-negative underlying

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2731359 http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In the two articles listed above we see several ways to extend the original ...
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49 views

The error term of Hagan's approximation of Black's vol in SABR

Hagans approximation of Black's implied vol in SABR is very! difficult to understand fully. But I want to ask in here if anyone can tell me more about the error term. Consider the paper: http://web....
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1answer
65 views

SABR Implied Vol: Normal Approximation vs Log-Normal Approximation

I am having trouble understanding the difference between the normal and log-normal implied volatilities from Hagans SABR model: http://web.math.ku.dk/~rolf/SABR.pdf. As far as i understand the main ...
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2answers
2k 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 $C_{BS}(F_0,K,T,\...
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36 views

Who came up with 3/2 SV model

Sorry, not a very quantitative question, but does anybody know who was the first person to write down and publish the 3/2 stochastic volatility model? I need this for a reference/bibliography.
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1answer
275 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
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1answer
44 views

$\beta = 1$: Simulation of SABR and whether a solution is *exact*

Quick question regarding the conditional distributions (SABR is just an example here) Consider $$dS_t = \sigma_tS_tdW_t$$ $$d\sigma_t = \alpha\sigma_tdV $$ $$dW_tdV_t=\rho dt$$ Hence a SABR process ...
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64 views

Taylor expansion of stochastic variables with dynamics of the form $dX_t=b(\sigma_t,X_t)dW_t$

https://www.math.nyu.edu/~cai/Courses/Derivatives/compfin_lecture_5.pdf In the above document stochastic taylor expansions are nicely explained. Let us now consider a typical SDE model in finance ...
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1answer
212 views

How to determine the risk-neutral measure in a Heston model?

To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're ...
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1answer
173 views

What's the point of stochastic volatiliy models if you can use local volatility? [duplicate]

Given known call option prices, there is a unique local volatility function consistent with those prices. So why use stochastic volatility models? We can use the market to find local volatility, and ...
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40 views

Why can't we create a “magic” basket of options to sell for no-arbitrage pricing in SVJ model?

I am learning how to price SVJ options and am reading some stuff on no-arbitrage pricing for SVJ model using the typical approach you would use (like in BSM option pricing) of creating a risk free ...
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61 views

What are good TEXTBOOK on stochastic volatility and interest rate theory?

I wanted to learn stochastic volatility modelling and interest rate modelling. On this site, a answer recommended me the books "Stochastic Volatilty Modelling" by Lorenzo Bergmo and "Interest Rate ...
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68 views

Simulating volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes

I am trying to simulate the volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes. In fact, giving $\mathbf{X}$ a $n$-dimensional vector ...
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282 views

Jim Gatheral's ansatz

In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes $$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$ where $\hat w_t:=\int_0^t \hat v_s ds$ is the expected total ...
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1answer
213 views

Mixing Black Scholes with SABR

I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp. I was wondering if the following ...
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40 views

Gatheral's SVI implementation in Java/Scala

I am trying to fit equity option implied vols using SVI model in Java, and I am using apache math commons library. Some of the option expiries fit very well, but others are completely off, and I am ...
3
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1answer
155 views

Dependence of implied volatility on spot-vol correlation

I have the following general SV model: $$ dS = \sigma S dW_S $$ $$ d\sigma = a(\sigma,t) dt + b (\sigma, t) dW_\sigma $$ $$ dW_S dW_\sigma = \rho dt $$ where $a , b$ are deterministic functions of $\...
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1answer
72 views

simple SABR model & negative strikes

My goal is to calibrate a simple SABR model. I do have $tenor$, $expiry$, $forward$ and "market volatilities for strike spread" ranging from -150 to 150 bps. I think the model can only be ...
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35 views

Vega computation in a stochastic volatility model

What are the possible strategies to compute analytically the Vega (not numerically) in a stochastic volatility model? The goal is to vega-hedge in a generic stochastic volatility model if possible, ...
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64 views

What are the go-to textbooks for advanced quant finance topics? [duplicate]

Credit risk, interest rate modelling, volatility modelling. What are the go-to books for each of these 3 topics in quant finance? The target audience should be someone who understands the basics of ...
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1answer
138 views

How to verify sticky delta property on a stochastic volatility model

Given a stochastic model for the evolution of St, with a given SDE for its volatility, how can you tell if the given model satisfy the sticky delta (or the sticky strike) property? Is it possible to ...
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113 views

Implied volatility as break-even delta hedge volatility

There have been some posts on this topic, but not what I am looking for, so a new post on an old topic.. I think some/most of us here are familiar with the following formula expressing implied ...
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138 views

SABR Question: Why does the market take the beta parameter as a constant?

SABR Question Why does the market take the $\beta$ parameter as a "constant"? I see most brokers quoting SABR parameters nowadays. I've seen many banks use $\beta$=0.5 as a rule. I've seen quants ...
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1answer
103 views

Please explain Heston Model parameters meaning [closed]

The Heston Model is given by: $$ dS_t = \mu S_t dt + \sqrt{v_t}S_tdB_{1t}$$ $$ dv_t = \kappa(\theta - v_t)dt + \xi \sqrt{v_t}dB_{2t}$$. The parameters are: $\theta$ is the long term variance $\...
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1answer
120 views

Bitcoin dynamics - C++ Simulation

I would like perform a simulation of Bitcoin future prices given a sample of the 4 past years (2014-2018). My problem is that I do not know what model to use! For common stocks I used the geometric ...
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1answer
91 views

Why Can I not estimate a CVAR from Heston Model

I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected ...
2
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1answer
103 views

Short time to maturity behaviour of implied volatility

There are several perturbative expansions in derivatives literature on the short-time to maturity behaviour of implied volatility. When it comes to implied volatility in (local) stochastic volatility ...
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0answers
102 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
2
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1answer
226 views

LSV model calibration with only few quotes per maturity

At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic ...
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1answer
427 views

Volatility swap hedge

What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging? I am aware of but have not yet read ...
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0answers
113 views

Using SVI model for IV surface

I am using well-known paper of J. Gatheral & A. Jacquier Arbitrage-free SVI volatility surface to explore SVI model. on the page 6 in the bottom is statet that The SVI-Jump-Wings (SVI-JW) ...
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57 views

Stochastic Long-Run Mean Instantaneous Variance in Heston Model (and extensions)?

I'm working on my dissertation in Financial Economics, focusing on the topic of Stochastic Volatility Jump Diffusion models; and I'm playing around with some ideas for model extensions. In particular, ...
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1answer
420 views

How to, from various hypotheses on the P&L, get known models (BS, Heston etc …)

Usually models in quantitative finance are taught by giving, let's say, stochastic differential equations, initial conditions, and then pricing, under the model, various derivatives written on the ...
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173 views

Mixed local-stochastic volatility model in Quantlib

At a conference the speaker mentioned that it is a standard approach today to use a mix of local and stochastic volatility model in equity, FX and interest rates. Can you please suggest the most ...
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0answers
45 views

The Free Boundary SABR: Natural Extension to Negative Rates

In the paper by Antonov, Konikov and Spector An alternative approximation for the SABR model is presented. I'm interested to implement the formula for the ATM swaptions implied volatilities in the ...
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3answers
248 views

How to show that SABR is log-normal for $\beta=1$ and normal for $\beta=0$?

For $\beta = 1$ SABR is log-normally distributed and for for $\beta = 0$ SABR is normally distributed. This is a very common property mentioned in almost every paper about SABR. But I can't find the ...
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142 views

Is SABR being used in practice for Equity options

Just to be clear: By "in practice" I mean what the banks and other financial companies do. Do financial companies use SABR for pricing equity options? Consider a stock with price $t$ being: $S_t$. ...
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3answers
384 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).
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1answer
92 views

Drift term in rough volatility models

I'm studying rough volatility papers and was wondering, why the drift term is always missing. See for example the paper Pricing under rough volatility by Bayer, Friz, Gatheral. On page 2, the ...
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1answer
82 views

When a stochastic volatility model is calibrated?

In an Investment Bank, how often a stochastic volatility model is calibrated ? Is it calibrated daily ? Is it calibrated whenever a pricing is required ? Thanks.
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1answer
157 views

Discretizing a Continuous Time Stochastic Volatility Model

How does the discrete time stochastic volatility model arise from the continuous time one? Also, forgive me for cross-posting. I have the following continuous time SDE for a stochastic volatility ...
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3answers
370 views

clarification to use collocation methods to get arbitrage free sabr

I'm reading the following two papers (first, second) which suggest a so called "stochastic collocation method" to obtain an arbitrage free volatility surface very close to an initial smile stemming ...
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1answer
281 views

SABR ATM volatility

The ATM implied volatility is important in SABR when calibrating the model. Let's consider the ATM vol (for a european call option): $$\sigma = \frac{\alpha}{f^{1-\beta}} \left[ 1+ \left(\frac{(1-\...
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3answers
4k views

Problems with local volatility models (vs stochastic volatility models)

Why is pricing with local volatility models are problem with exotics, mainly due to "the volatility surface is the market's current view of volatility and this will change in the future meaning the ...
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0answers
67 views

Does the Asian Option (average Option) depend on the forward implied vol

I can easily understand that the forward starting Option and Barrier Option depend on the forward implied vol smile at resetting date, so we always choose the stochastic vol model for underlying to ...