MONOTONICITY IN THE VOLATILITY OF SINGLE-BARRIER OPTION PRICES

Jonatan Eriksson ()
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Jonatan Eriksson: Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 06, 987-996

Abstract: 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.

Keywords: Barrier option; convexity; volatility; parabolic equation (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024906003822

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