Suppose V () is the option price function with dependence on volatility . Show that V (o)
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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 > σimp and V” imp, where σimp 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).
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