FKaria
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Does implied vol vary for calls vs puts?
Accepted answer
22 votes

Taking away all frictions and incomplentess of the market, the theory says that European Call and Puts do have the same implied volatility unless there is an arbitrage opportunity by put call parity $...

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How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?
6 votes

Just following Musiela Rutkowski (the link redirects to Amazon). The risk neutral measure is derived form imposing that the present value of a self financed portfolio (i.e.; no infusion or withdraw of ...

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Price of a down-and-out call in terms of European call
5 votes

No, you cannot decompose a barrier option as a linear combination of European options. You can find the derivation of the formula in Musiela & Rutkowsi pg.235, for example. But I can tell you ...

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Extrapolating implied volatilities to small time
4 votes

A really simple and arbitrage free solution is to extrapolate flat volatility on the same moneyness. Let's say that you want an implied volatility for strike $K$ at time $t<t_1$, and $t_1$ is the ...

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How to calculate stock move probability based on option implied volatility and time to expiration? (Monte Carlo simulation)
4 votes

I think that you may be looking for $$ \mathbb{P}(S_T<K) = \frac{\partial P}{\partial K}(K) = 1 + \frac{\partial C}{\partial K}(K) $$ where $P(K)$ and $C(K)$ are the european put and call ...

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Reference request for arbitrage pricing with martingale theory
2 votes

I don't think there many books that proof the fundamental theorem of asset pricing as is quite technical and not very interesting for the usual audience studying quantitative finance. Also, Ito ...

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Value of American Call vs Value of European Call when using implicit finite differences
Accepted answer
2 votes

I guess that, in your model, the stock does not pay dividends. The price of an European Call option written for a stock that does not pay dividends is always higher than its intrinsic value. ...

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Stochastic modeling of stock price process
2 votes

There are many, which are mostly generalizations of the Black-Scholes model (Geometric Brownian Motion). For Equity stocks, the most widely used (IMHO) is the deterministic generalization of Black-...

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Basket Option weight sensitivity calculation
1 votes

I would define the weights $w_1,\ldots,w_n$ as whatever number you want and the basket given by $$ B_t = \sum_{i=1}^n \frac{w_i}{W}S_t^{(i)}\ , \qquad W = \sum_{i=1}^nw_i $$ so the weights always sum ...

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How to transform process to risk-neutral measure for Monte Carlo option pricing?
1 votes

You don't have to believe anything. The simulations are risk-neutral if the expectation at any date divided by the spot price is the return of a risk free zero-coupon bond. That's everything (the only ...

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