Consider an asset with value Sm at time-step mt and expected value Sm+1 under a continuous...

2. 
    

Transcribed Image Text:

Consider an asset with value Sm at time-step môt and expected value Sm+1 under a continuous random walk model, 00 E₁[Sm+1|Sm] = ["S'p(S™‚m&t; S', (m + 1)&t)dS', 0 where p(S,t; S't') is the probability density function p(S, t; S't') = 1 e-(log(S/S)-(r-20²)(t'-t))²/20² (t'-t) OS'√2π(t' - t) for a risk-neutral random walk. Show that ε [Sm+1| Sm] = erεtsm Hint: use Sex and then complete the square in the exponent. Consider an asset with value Sm at time-step môt and expected value Sm+1 under a continuous random walk model, 00 E₁[Sm+1|Sm] = ["S'p(S™‚m&t; S', (m + 1)&t)dS', 0 where p(S,t; S't') is the probability density function p(S, t; S't') = 1 e-(log(S/S)-(r-20²)(t'-t))²/20² (t'-t) OS'√2π(t' - t) for a risk-neutral random walk. Show that ε [Sm+1| Sm] = erεtsm Hint: use Sex and then complete the square in the exponent.

Answer rating: 100% (QA)

1 As given the probability density function for a conti... View the full answer