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5 votes
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Asymptotics of Call Option as $S\to0$

This is more of a math question than a quant question. Under Black Scholes dynamics (assuming $r=0$ for simplicity), as everyone knows we have $$C=SN(d_1)-KN(d_2)$$. In this case, we are interested ...
dm63's user avatar
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1 vote

Asymptotics of Call Option as $S\to0$

I'm not 100% sure, please double-check. I think that both in the ITM and the OTM case (requested), a model-free answer cannot exist. In particular, the rate at which: ITM: $C(S_0) \rightarrow S_0$ as ...
Gabriele Pompa's user avatar
1 vote

Asymptotics of Call Option as $S\to0$

Edit: the original question didn't specify "model independence" and so the below focuses on the BS framework. Also, i focused on speed of convergence rather than order of convergence: I will ...
Jan Stuller's user avatar
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