# Black-Scholes option pricing [duplicate]

Consider Black-Scholes (B, S) market model. Let $$r = 0$$ (hence, $$B_t ≡ 1$$), $$S_0 = 0$$.
Stock price is described by $$dS_t = σS_tdW_t$$.
Find the price of the option that pays $$(S_T^3 - S_T^2 )_+ = max(S_T^3 - S_T^2, 0)$$.

Any help on how exactly to apply Girsanov here?

• Apparently it is different, because $S_t$ is a martingale, but $S_t^2$ is not.
– Kyle
Commented Jul 19, 2021 at 9:40
• yes, $S_t$ is a martingale but I don’t see why the standard approach wouldn’t work just because $r=0$. Commented Jul 19, 2021 at 9:48
• I also think that the link provided by Kevin gives you the approach: 1) Split up the expectation using the indicator function. 2) Use the measure where $S_t^3$ is numeraire for the first part of the expectation. 3) Use the measure where $S_t^2$ is numeraire for the second part of the expectation. Commented Jul 19, 2021 at 10:14
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