Suppose that the stock price S, follows lognormal distribution St= Soe(a-8-0.50) t+oiz Prove that the conditional...

 

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Suppose that the stock price S, follows lognormal distribution St= Soe(a-8-0.50²) t+o√iz Prove that the conditional expectation of lognormal prices, when terminal stock price ST falls below Kis where d₁ = d₂ = E(ST ST < K) = Soe(a-s)r N(-d₁) N(-d₂) In(So/K) + (a-6 +0.50²)T OVT In(So/K) + (a-8-0.50²)T αντ =d₁ - o√T Hints: E(ST ST < K) is defined as E(ST STK) = = E [ST1{ST<K}] Pr(ST < K) Suppose that the stock price S, follows lognormal distribution St= Soe(a-8-0.50²) t+o√iz Prove that the conditional expectation of lognormal prices, when terminal stock price ST falls below Kis where d₁ = d₂ = E(ST ST < K) = Soe(a-s)r N(-d₁) N(-d₂) In(So/K) + (a-6 +0.50²)T OVT In(So/K) + (a-8-0.50²)T αντ =d₁ - o√T Hints: E(ST ST < K) is defined as E(ST STK) = = E [ST1{ST<K}] Pr(ST < K)

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