Questions tagged [stochastic-volatility]
The stochastic-volatility tag has no usage guidance.
367
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How to project 1 Year ATM Implied volatility for SPX 500 1Year from now? Final goal is to calculate 1 Year Call prices on SPX 500 1 year from now?
I have the historical data for 1Year ATM Implied Volatility on SPX 500. I want to simulate the 1 year call option prices 1 year from now. What methods and approaches do I need to use? (Heston,GARCH, ...
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Numerical simulation of Bates model (Monte Carlo)
I'm trying to build Bates model in Python!
$$dS_{t} = \mu S_{t} dt + \sqrt{V_{t}}S_{t}dW_{t}^{1} + J_{t}dQ_{t}$$
$$dV_{t} = \kappa(\theta - V{t})dt + \eta \sqrt{V_{t}}dW_{t}^{2}$$
$$dW_{t}^{1}dW_{t}^{...
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Are there volatility models dependent on returns?
When I look at the relationship between volatility and price, I see a clear negative correlation as shown in this figure (SPY and VIX prices today looking back 1 year).
The common volatility models (...
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Stochastic Volatility Models Real World Calibration
I am trying to find some research pertaining to the historical (or real world) calibration of stochastic volatility models.
For example, in applications such as counterparty credit risk (IMM) or ...
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Solve the following SDE: $\mathrm{d}X_t = a(b-X_t) \,\mathrm{d}t + c X_t \, \mathrm{d}W_t$
Let $\mathrm{d}X_t = a(b-X_t) \,\mathrm{d}t + c X_t \, \mathrm{d}W_t$ be a stochastic differential equation where $a$, $b$, and $c$ are positive constants, so I tried to solve it but I got stuck in ...
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Robust bounds or approximations on implied volatility skew when $\lvert \rho \rvert \rightarrow 1$
Are there any robust / non-parametric results for pure stochastic volatility models, in terms of bounds or preferably accurate approximation, for the implied volatility skew $\partial IV(k) / \partial ...
user34971
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Anyone working on rough volatility modelling? Need relevant books to read
Just wondering if there is anyone working in the field of rough volatility?
I know the rough volatility modelling is quite new in the field. Can I get some books recommendation to go through?
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Does the Heston calibration have to be done on an arbitrage-free surface?
In a similar way to local volatility?
I'm trying to calibrate a surface, but the results aren't convincing, so I was wondering if it was necessary to first use a way to regulate it (splines, ...
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how to calculate implied volatility
I have some options prices I found using the Heston Model. How do I calculate the implied volatility? In Matlab there exist a blsimpv function, but is this the right tool for me since I'm working with ...
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Computing Itô differential of conditional expectation process (Heston SDE)
Going through this article
on Heston's model, where the variance evolves following the SDE
\begin{equation}
\label{sd1}
d\sigma^2_t = \kappa \bigg( m - \color{red}{\sigma^2_t} \bigg)dt + \nu \sqrt {\...
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Is Local Stochastic Vol needed in order to price barrier options?
I'm trying to understand when it is appropriate to use stochastic local volatility models rather than local volatility ones.
More precisely, for which products is it appropriate to introduce a ...
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How many options would be required to dynamically replicate the VIX nowadays?
The VIX is a portfolio of OTM options on the SPX with non-zero quotes.
From CBOE white-paper:
Only SPX options quoted with non-zero bid prices are used in
the VIX Index calculation. [...] As ...
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How to correctly simulate volatility shocks?
I am working on the comparison of different volatility timing/target strategies on portfolios starting from different conditions (data, asset classes, calculation of realized volatility, different ...
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Different volatility surface ( Local vol, Stochastic vol etc.)
Despite many questions about local and stochastic volatility available on this forum, i still have a few doubts left. Essentially I am seeking validation whether I am interpreting things correctly.
...
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Stochastic Vol Mathematical derivation [closed]
I want to understand the mathematical steps done. Can someone please simplify the derivation of d(pi) from Pi? Thanks in advance.
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Stochastic Volatility and Sticky Delta
"Stochastic volatility models can be thought of as sticky delta model. And Local volatility model as sticky Strike." Please help me understand how the author has reached this conclusion.
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Local volatility and Stochastic Volatility
Please help me understand similarity and differences between local volatility and Stochastic Volatility both intuitively and mathematically.
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What is the intuition behind "jumps" causing volatility skew?
Some models use jumps as a way to explain volatility skew. I understand that if jumps exist, then you are "mishedged" as you no longer can continuously hedge. Options have a gamma component and ...
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Volatility of a perpetuity $E\Big[\Big(\int_0^\infty e^{-ks+mz_s}ds\Big)^\eta\vert\mathcal{F}_t\Big]$
Let $z$ be a brownian motion, let $\mathcal{F}$ be the filtration it generates. For $k>0$ and $m\in\mathbb{R}$, I define the process $Y$ as
$$Y_t=E\Big[\Big(\int_0^\infty e^{-ks+mz_s}ds\Big)^\eta\...
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What models are used for pricing cliquet options (esp. for Asian Equity underliers)? How good is Bergomi model?
What are the most common models, actually used by trading desks for Asian underliers, for pricing cliquet options?
I would like to know both - (1) the production model used for daily P&L, and ...
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Caplet price under stochastic volatility is the black price integrated over volatility distribution
Hull&White 1987 state that when the brownian motion driving the volatility and the brownian motion driving the forward rate are uncorrelated, the caplet price under stochastic volatility is the ...
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Bond Option Hedging
(My question)
Please show me how to solve from (2) to (4) with computation processes.
These are too difficult to solve.
Thank you for your help in advance.
(Cross-link)
I have posted the same ...
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Cumulative Integration with regard to Vasicek Model's Bond Price and its Forward Price
(My Question)
Please show me how to compute the following expectation with its computation process. Besides, $B_t$ is S.B.M.
$$E\left[ \exp \left( - \int^T_t \int^u_0 \sigma e^{-b(u-s)} d B_s du \...
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Why do we fit volatility surfaces implied from a option pricing model to the empirical data?
As far as I understand volatility surface. It is made of 2 components, the volatility skew/smile and the volatility term structure. Together they form something like
Implied volatility is ...
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The Riccatti equation for The Cox-Ingerson-Ross Model
(My Question)
I went through the calculations halfway, but I cannot find out how to calculate the following Riccatti equation. Please tell me how to calculate this The Riccatti equation with its ...
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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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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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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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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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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.
user34971
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$\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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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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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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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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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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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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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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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 ...
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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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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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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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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 ...
user34971
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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
$$
where $a , b$ are deterministic functions of $\...
user34971
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Please explain Heston Model parameters meaning [closed]
The Heston Model is given by:
$$ 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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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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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 ...
user34971
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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 ...
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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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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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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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