Well "based on option pricing" is a little vague, but the desired solution is probably to use one of the stocks (say stock $B$) as your numeraire. If you're unfamiliar the intuitive idea is that ...

Under the stock numeraire measure, $\frac{B_t}{S_t}$ is a Martingale. We can compute $$d\frac{B_t}{S_t}= \frac{1}{S_t}dB_t -\frac{1}{S_t^2}B_tdS_t+\frac{1}{S_t^3}B_t\sigma^2S_t^2dt\\=\frac{B_t}{S_t}\... View answer 5 votes There is one condition under which the risk neutral probability of an event can be zero: if the real world probability is zero. If not then any contract that pays off in that event must go down in ... View answer Accepted answer 4 votes The price is, under the risk-neutral measure,$$ P_t = e^{-r(T-t)}\mathbb E[S_T^1 \mathbb 1(S_T^2\le K)\mid \mathcal F_t].$$Since the risk-neutral asset processes are independent geometric brownian ... View answer Accepted answer 4 votes You have forgotten the combinatorial factors for binomial probabilities on your terms. You need$$ {n\choose k} p^n(1-p)^{n-k},$$not just$$ p^n(1-p)^{n-k}.$$The second term should have a factor of ... View answer Accepted answer 3 votes You sell it and buy a new one. It does not expire. This is conceptually no different from rolling futures if you're more familiar there. It seems you haven't gotten the gist of the other answer so I'... View answer 2 votes I think you would know better than me. But assuming this is some sort of riddle, I would say you made money by dynamically hedging the straddle. When the stock goes into the money your straddle delta ... View answer Accepted answer 2 votes Imagine you hold a zero coupon bond with a certain maturity T and the short rate follows a process like you specified. You might know deterministically what the cash bond pays this period, but you ... View answer 1 votes I think your calculation is right and the Kelly criterion is very aggressive. Note however that it is meant to apply to the situation where you win exactly your last bet times 299 84% of the time and ... View answer 1 votes Remember$$ d_1 = \frac{\log(S/K) + \left(r+\frac{1}{2}\sigma^2\right)T}{\sigma\sqrt{T}}$$so the first term is decreasing in T. Let's take the derivative:$$\frac{\partial \delta}{\partial T} = N'(...
Ito's lemma gives $$dF = \left(\frac{\partial F}{\partial t}+\frac{1}{2}\frac{\partial^2F}{\partial S^2}\sigma^2 S^2\right)dt + \frac{\partial F}{\partial S}dS = adt + bdS$$ Using the usual rules, e....