FKaria
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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 $... View answer 6 votes Just following Musiela Rutkowski (the link redirects to Amazon). The risk neutral measure is derived form imposing that the present value of a self financed portfolio (i.e.; no infusion or withdraw of ... View answer 5 votes No, you cannot decompose a barrier option as a linear combination of European options. You can find the derivation of the formula in Musiela & Rutkowsi pg.235, for example. But I can tell you ... View answer 4 votes A really simple and arbitrage free solution is to extrapolate flat volatility on the same moneyness. Let's say that you want an implied volatility for strike$K$at time$t<t_1$, and$t_1$is the ... View answer 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 ... View answer 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 ... View answer 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. ... View answer 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-... View answer 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 ...