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Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed Dynamic-Static Hedging
Pricing of Securities · Submitted 16 Sep 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim While in this paper we apply our framework to an incomplete market version of the credit-equity Merton's model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options.
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We study the problem of optimal pricing and hedging of a European option written on an illiquid asset $Z$ using a set of proxies: a liquid asset $S$, and $N$ liquid European options $P_i$, each written on a liquid asset $Y_i, i=1,N$. We assume that the $S$-hedge is dynamic while the multi-name $Y$-hedge is static. Using the indifference pricing approach with an exponential utility, we derive a HJB equation for the value function, and build an efficient numerical algorithm. The latter is based on several changes of variables, a splitting scheme, and a set of Fast Gauss Transforms (FGT), which turns out to be more efficient in terms of complexity and lower local space error than a finite-difference method. While in this paper we apply our framework to an incomplete market version of the credit-equity Merton's model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the problem of optimal pricing and hedging of a European option written on an illiquid asset $Z$ using a set of proxies: a liquid asset $S$, and $N$ liquid European options $P_i$, each written on a liquid asset $Y_i, i=1,N$. | contribution 0.59 | 0.56 | 0.04 | asserted 0.94 |
| s1 | We assume that the $S$-hedge is dynamic while the multi-name $Y$-hedge is static. | method 0.97 | 0.61 | 0.04 | asserted 1.00 |
| s2 | Using the indifference pricing approach with an exponential utility, we derive a HJB equation for the value function, and build an efficient numerical algorithm. | method 0.85 | 0.96 | 0.15 | asserted 1.00 |
| s3 | The latter is based on several changes of variables, a splitting scheme, and a set of Fast Gauss Transforms (FGT), which turns out to be more efficient in terms of complexity and lower local space error than a finite-difference method. | method 0.97 | 0.91 | 0.11 | asserted 0.99 |
| s4 | While in this paper we apply our framework to an incomplete market version of the credit-equity Merton's model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options. | future work 0.52 | 0.42 | 0.16 | hedged possibility 0.83 |
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The paper
Original abstract
We study the problem of optimal pricing and hedging of a European option written on an illiquid asset $Z$ using a set of proxies: a liquid asset $S$, and $N$ liquid European options $P_i$, each written on a liquid asset $Y_i, i=1,N$. We assume that the $S$-hedge is dynamic while the multi-name $Y$-hedge is static. Using the indifference pricing approach with an exponential utility, we derive a HJB equation for the value function, and build an efficient numerical algorithm. The latter is based on several changes of variables, a splitting scheme, and a set of Fast Gauss Transforms (FGT), which turns out to be more efficient in terms of complexity and lower local space error than a finite-difference method. While in this paper we apply our framework to an incomplete market version of the credit-equity Merton's model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options.
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This work is an extension of our paper [ref] where the following problem was considered.
Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging · Introduction · 0.99
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Similar to [ref] , we use the indifference pricing approach and an exponential utility function to derive a HJB equation for the value function.
Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging · Introduction · 0.93
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