# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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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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### Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
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### 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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### Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
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### Likelihood ratio and pathwise sensitivity method for coupled SDEs

I have two coupled SDEs \begin{align*} dS_t=rS_tdt+V_tdW_t^{(1)},\\ dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\ \end{align*} where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
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### Has a closed-form formula for the collateral choice option been found?

The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
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### Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure

I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler ...
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### recent developments in American options?

I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based ...
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### Importance sampling for Monte Carlo with local volatility in practice

I am given a diffusion with a local volatility to price barrier options: $$dX(t)=X(t)\mu dt+X(t)\sigma(t,X)dW_t$$ I want to use Importance Sampling to price barrier options "far" out of the ...
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### Libor Market Model with SABR Calibration

What is the industry practice in calibrating SABR Libor Market Model? Do you first calibrate the SABR model using market data and then implement the libor market model with the calibrated parameters? ...
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### Intuition behind the Carr and Wu (2014) static hedging for ordinary options

Let $(S_t)_{t \geq 0}$ be the price of an underlying asset, $r$ be the risk-free rate of return, $q$ the dividend yield, $C_t(K,T)$ is the price of a call option written on $S_t$ at time $t$ with ...
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### Pricing interest rate options in emerging markets

I've been thinking how to price the early payment of mortgages in banks from emerging markets, where swaptions/caps/floors aren't available, and how to hedge this kind of options. At first I thought ...
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### How are quants able to verify whether their calculated prices are any good

This question is related to the discussion on Model Validation Criteria However it appeard to be very high level to me and I would like to go more into detail. Not working at a pricing desk the ...
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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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### Best Method (Or Just a Good Method) of Predicting Intraday Volatility in Real Time?

I apologize if this is a stupid question, I'm a complete neophyte in academic finance but I am trying to learn. I am trying to create an estimate of how likely indexes are to rise/fall by x% by the ...
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### Probability density from COS method too sensitive to truncation range

I have a long-standing confusion around the truncation range of the COS method proposed by Fang and Oosterlee because I find that the results are highly volatile given the different truncation ranges. ...
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### Very close local volatility and implied volatility using Dupire's equation

I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
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### Why Vasicek model on a tree is a bad choice for pricing American option on credit prepayment?

I have an American option on a credit prepayment, i.e. the holder of the option can prepay the remaining credit if the interest rate falls below the initial strike. The pricing of this option was done ...
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### Integrated Delta does not seem to be smooth (ATM, Heston)

I am interested in an integrated call option that removes the dependence on time, $$I(S)=\int_0^\infty C(S,t)\text{d}t.$$ Because the value of a call option is a smooth function, I expect this ...
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### Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
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### 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 ...
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### 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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### How can a beginner trader make use of 'volatility of volatility'

For a beginner option trader in equity options, how can he use this metric that is provided by his broker/data vendor? How can he use this metric to gain an added understanding of the option pricing/...
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### negative transition probabilities in the heston model

I've been trying to implement a bivariate tree for pricing american options with the heston model in R using the paper of Beliaeva and Nawalkha (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
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### ATM volatility versus OTM volatility and directional standard deviation

The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put). Is there a smaller standard deviation (in price terms) to ...
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### Models for tick-by-tick / high-frequency data

I've spoken to one or two persons at some market making shops, and I'm under the impression that for modelling tick data, aside from the rise of ML, a pure jump process such as the variance gamma ...
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