Questions tagged [geometric-brownian]

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6
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4answers
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Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
2
votes
2answers
313 views

Market price of risk on two assets

Under the assumptions of the Black--Scholes model, I read that the market price of risk of two assets $S_1$ and $S_2$ are the same, if they both follow Geometric Brownian motion driven by the same ...
1
vote
1answer
79 views

Copula analytic formula for $max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}}$

Consider the payoff function $$ V_T = max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}} = (S_T^1 - K)1_{\{S_T^1 > K\}}1_{\{L<S_T^2<U\}}$$ where $S_T^1$ and $S_T^2$ are two GBM distributed stocks with ...
1
vote
1answer
127 views

Probability of an Option maturing In-the-money vs. Volatility

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ...