Monotonicity in the volatility of single-barrier option prices
2006 (English)In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 9, no 6, 987-996 p.Article in journal (Refereed) Published
We generalize earlier results on barrier options for puts and calls and log-normal stock processes to general local volatility models and convex contracts. We show that Γ ≥ 0, that Δ has a unique sign and that the option price is increasing with the volatility for convex contracts in the following cases:
If the risk-free rate of return dominates the dividend rate, then it holds for up-and-out options if the contract function is zero at the barrier and for down-and-in options in general.
If the risk-free rate of return is dominated by the dividend rate, then it holds for down-and-out options if the contract function is zero at the barrier and for up-and-in options in general.
We apply our results to show that a hedger who misspecifies the volatility using a time-and-level dependent volatility will super-replicate any claim satisfying the above conditions if the misspecified volatility dominates the true (possibly stochastic) volatility almost surely.
Place, publisher, year, edition, pages
2006. Vol. 9, no 6, 987-996 p.
Barrier option, convexity, volatility, parabolic equation
IdentifiersURN: urn:nbn:se:uu:diva-93999DOI: 10.1142/S0219024906003822OAI: oai:DiVA.org:uu-93999DiVA: diva2:167674