Suppose V () is the option price function with dependence on volatility . Show that V (o)

Suppose V (σ) is the option price function with dependence on volatility σ. Show that 

where σ₁ is given by (3.5.25). Hence, deduce that V” > 0 if σ₁ > σ_imp and V” imp, where σ_imp is the implied volatility. Explain why V (σ) is strictly convex if σ₁ > σimp and strictly concave if σ₁ imp, and deduce that

for both cases (Manaster and Koehler, 1982).

Transcribed Image Text:

V" (o) = V'(o)t 403 (oo) for all o,