Question
This problem aims to show that the discounted stock price (of a non-dividend paying stock) is a martingale under the risk-neutral measure in the Black-Scholes
This problem aims to show that the discounted stock price (of a non-dividend paying stock) is a martingale under the risk-neutral measure in the Black-Scholes setting. Recall that the stock price satises the following SDE under the risk-neutral measure ~ P dS ( t ) = S ( t )( rdt + d ~ Z t ) where ~ Z is a standard Brownian motion under the risk-neutral probability measure P . Dene Y ( t ) = e^ (-rt) S ( t ) : Find the SDE that Y must satisfy (using It^o's lemma). Note that the drift of Y is equal to zero. Hence, the It^o process Y is a martingale.
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