# Tagged Questions

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### How to show that this weak scheme is a cubature scheme?

Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
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### 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 ...
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### 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 ...
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### SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
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### SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW. To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model....
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### 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 ...
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### Obtaining a consistent covariance matrix for stochastic volatility processes

What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix? I read in Hull that in order to have a consistent covariance matrix, volatility parameters ...
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### arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy $$dB_t = B_t r dt$$ \quad \quad \quad \quad \, ...
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### 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 ...
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### relation between asset's and equity volatilities - merton model

In terms of Merton credit risk model need to find the initial value of counterparty's assets and the volatility of the assets. Both value are not directly observable thus we have to approximate them ...
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### What is the rationale behind using SV models with 2 distinct volatility processes?

In the Double Heston model, there are 2 distinct volatility processes. The SDEs read \begin{align} & d{{S}_{t}}=r{{S}_{t}}dt+\sqrt{{{v}_{1}}(t)}{{S}_{t}}d{{W}_{1}}(t)+\sqrt{{{v}_{2}}(t)}{{S}_{t}}...
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### CIR model problem - deriving PDE, Feynman-Kac

I am reviewing a CIR model problem, where $r_t$ has following dynamics $$dr_t=a(b-r_t)dt+\sigma \sqrt{r_t} dW_t^* \quad \quad (1)$$ for some constants $ab>\frac{\sigma^2}{2} \quad$ Letting T ...
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### SABR model inconsistent with Black Swaption Pricing

I am confused on the following: When we price swaption, the market convention is to use Black's Model which assumes forward swap rate is following Black's model under the Q(t) measure. When we tries ...
Suppose we have : $\frac{dS_{t}}{S_{t}}= \sigma dW_{t}$ with $\sigma_{t}$ a stochastic volatility process. How to compute $\mathbb{E}^{Q}[(S_{T}-K)+]$ ? Is there a BS alike formula : "\$S_{0}N(d+)-Ke^{-...