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Keywords = down-and-out

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17 pages, 401 KB  
Article
Pricing Path-Dependent Options under Stochastic Volatility via Mellin Transform
by Jiling Cao, Xi Li and Wenjun Zhang
J. Risk Financial Manag. 2023, 16(10), 456; https://doi.org/10.3390/jrfm16100456 - 20 Oct 2023
Viewed by 2916
Abstract
In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction [...] Read more.
In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction term, we use Mellin transform. We also conduct a sensitivity analysis on these formulas, and compare the option prices calculated by them with those generated by Monte-Carlo simulation. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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20 pages, 567 KB  
Article
Time-Discrete Hedging of Down-and-Out Puts with Overnight Trading Gaps
by Rainer Baule and Philip Rosenthal
J. Risk Financial Manag. 2022, 15(1), 29; https://doi.org/10.3390/jrfm15010029 - 11 Jan 2022
Cited by 1 | Viewed by 5417
Abstract
Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the [...] Read more.
Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the hedge portfolio can only be adjusted in discrete time intervals. In this paper, we analyze this hedging situation, especially the case of overnight trading gaps. We show how a position in a short-term vanilla call option can be used for efficient hedging. Using a mean-variance hedging approach, we calculate optimal hedge ratios for both the underlying and call options as hedge instruments. We derive semi-analytical formulas for optimal hedge ratios in a Black–Scholes setting for continuous trading (as a benchmark) and in the case of trading gaps. For more complex models, we show in a numerical study that the semi-analytical formulas can be used as a sufficient approximation, even when stochastic volatility and jumps are present. Full article
(This article belongs to the Special Issue Structured Financial Products and Derivatives)
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