# Questions tagged [risk-neutral-measure]

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### Model-Free Option Pricing

From Breeden and Litzenberger (1978) and subsequent work, we may find the risk-neutral density $q_{S_T}$ of $S_T$ from European option prices - assuming there are enough traded options (e.g. SPX) via ...
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### Valuation of Cash-Or-Nothing option

Studying options pricing, I'm stuck with the following problem: The price of a stock is described by the dynamic: $$dS_t = \mu\, dt + \sigma\,dW_t$$ Compute the fair price of a Cash or Nothing ...
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### Risk neutral measure & change in numeraire

There are two questions about risk neutral and change in numeraire I am not so sure if my answer is correct. Question 01: Risk neutral Let says I have 2 risky asset A and B. Each has stochastics ...
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### What discount rate should I use in domestic/foreign context?

I am trying to price a quanto option by monte carlo simulation via quanto adjustment. SDE: $dS_t^f=S_t^f(r_f - \rho \sigma_s \sigma_{d/f})dt + S_t^f\sigma_s dW_t^d$, where $S_t^f$ is the underlying ...
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### How can the forward risk neutral measure be used to derive Black's model?

In the Hull textbook's derivation of Black's model (Section 27.6), they apply equation (27.20), which is $f_0 = P(0,T)E_T(f_T)$, where $P(0,T)$ is the value of a zero coupon bond at time $0$ expiring ...
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### Equivalence of Put Pricing Formulas

I have to show that: \begin{equation} P_{t,T}(K)=e^{-r(T-t)} \int_0^{\infty}\left(K-S\right)^+ q_T^S(S)dS \end{equation} is equivalent to: \begin{equation} P_{t,T}(K)=e^{-r(T-t)}\int_{-\infty}^{...
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### Risk-neutral pricing and statistical arbitrages

I'm studying the martingale approach to asset pricing. Dealing with the concept of risk-neutral probability, I came up with a question about the possibility of "arbitrages in expectation". I'll be ...
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