# Tagged Questions

Questions about models for the valuation of option contracts.

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### Real world monte-carlo (P-measure)

Consider the 2 following approaches to pricing a security: Monte-carlo ($\mathbb{Q}$-measure) $$$C = \frac{1}{N} \sum_{i=1}^{n} e^{-rT} max(S_i(t) - K, 0)$$$ Monte-carlo ...
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### Examples for the option model validation

When implementing a code for the new model, even if it provides sensible price, it is still a good idea to compare it against some benchmarks, even in the special case of constant volatility Black-...
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### Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma \sigma}b^2(\sigma)+\frac{...
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### Price of an American call option [closed]

I'm working through revision questions at the moment and we are asked to compute the price of an American call option. Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$ Let $0<U<T$ be fixed ...
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### Importance Sampling - where to center the sampling distribution?

Consider a Monte Carlo (MC) approximation to a European call with BS parameters $r = 0.05, \sigma = 0.4, T = 10, S_0 = 50$ and $K = 95$. Consider the following results, each using 1M points: plain ...
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### Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...