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Monotonicity in the...
Monotonicity in the volatility of single-barrier option prices
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- Eriksson, Jonatan (författare)
- Uppsala universitet,Matematiska institutionen
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(creator_code:org_t)
- 2006
- 2006
- Engelska.
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Ingår i: International Journal of Theoretical and Applied Finance. - 0219-0249. ; 9:6, s. 987-996
- Relaterad länk:
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https://urn.kb.se/re...
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visa fler...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Barrier option
- convexity
- volatility
- parabolic equation
- MATHEMATICS
- MATEMATIK
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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