spaceisdarkgreen
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How to price this option?
7 votes

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 ...

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Change-of-measure: Dynamics of $\log(S_t)$ with $S_t$ as numeraire
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6 votes

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}\...

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Why risk neutral probabilities should be strictly greater than zero for no arbitrage condition?
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 ...

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Pricing for an Odd Type of Asset or Nothing Option
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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 ...

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Put-Call Parity on Currency and Binomial Trees
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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 $...

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What does rolling a CDS entail?
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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'...

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Positive PnL with long volatility strategy
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 ...

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Short-rate models: Risk-premium of $T$-bonds
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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 ...

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Can a Kelly Criterion Percent be very high?
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 ...

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ITM call delta when T increases
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'(...

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minimum variance hedge with stochastic processes
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1 votes

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....

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