Pricing Vulnerable Options with Stochastic Volatility and Stochastic Interest Rate

Yue, Shengjie; Wu, Hui; Ma, Yong

doi:10.1007/s10614-019-09929-4

Cited by 18 publications

(6 citation statements)

References 27 publications

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“…Actually, Heston SV model has been considered one of the most popular substitutions in pricing fnancial derivatives (see e.g., Ma et al [17], Kim et al [18], Levendis and Eben [19], He and Lin [20], and He and Chen [21]). Te Heston model assumes that the volatility of an underlying asset is not constant and allowed to follow a square root process, which can be correlated with the Brownian motion driving the asset price itself.…”

Section: Introductionmentioning

confidence: 99%

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

Deng

2023

Mathematical Problems in Engineering

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In this paper, we consider the pricing problem for the extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of the logarithm of two asset prices is derived by using the Feynman–Kac theorem and one-order Taylor approximation expansion. The semiclosed analytical pricing formulas of the European extremum options including option on maximum and option on minimum of two underlying assets are derived by using measure change technique and Fourier transform approach. Some numerical examples are provided to analyze the pricing results of extremum options under affine model, nonaffine model, Black–Scholes model, and the influences of some model parameters on the option. Numerical results show that the analytical pricing formulas have higher computational efficiency and accuracy than those of Monte Carlo simulation method. Also, results of sensitivity analysis report that the nonaffine models are more effective than other existing models in capturing the effect of volatility on option pricing.

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Section: Introductionmentioning

confidence: 99%

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

Deng

2023

Mathematical Problems in Engineering

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“…With these results, there have been many studies on the improvement of the pricing model for the vulnerable option under the structural model. Models such as the stochastic interest rate model [4], early counterparty risk model [5,6], stochastic volatility model [7][8][9][10] and jump-diffusion model [11][12][13][14] have been used to extend the pricing models of vulnerable options under the structural model. In addition, the pricing models of vulnerable options under the reduced-form model have been studied in recent years.…”

Section: Introductionmentioning

confidence: 99%

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

Jeon

Kim

2021

Mathematics

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In this paper, we study the valuation of power exchange options with a correlated hybrid credit risk when the underlying assets follow the jump-diffusion processes. The hybrid credit risk model is constructed using two credit risk models (the reduced-form model and the structural model), and the jump-diffusion processes are proposed based on the assumptions of Merton. We assume that the dynamics of underlying assets have correlated continuous terms as well as idiosyncratic and common jump terms. Under the proposed model, we derive the explicit pricing formula of the power exchange option using the measure change technique with multidimensional Girsanov’s theorem. Finally, the formula is presented as the normal cumulative functions and the infinite sums.

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“…Klein [10] extended the result of [9] by considering the correlation between the firm value process of the option issuer and the underlying asset process of the option. Based on the work of [10], there have been many extended results on vulnerable options with models such as the stochastic interest rate model [11], the early counterparty risk model [12,13], the stochastic volatility model [14][15][16][17], and the jump-diffusion model [18][19][20][21]. Furthermore, many researchers have studied vulnerable exotic options such as the American option [22], the Asian option [23], the exchange option [24], and the path-dependent option [25] under the structural model.…”

Section: Introductionmentioning

confidence: 99%

Valuation of Exchange Option with Credit Risk in a Hybrid Model

Kim

2020

Mathematics

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In this paper, the valuation of the exchange option with credit risk under a hybrid credit risk model is investigated. In order to build the hybrid model, we consider both the reduced-form model and the structural model. We adopt the probabilistic approach to derive the closed-form formula of an exchange option price with credit risk under the proposed model. Specifically, the change of measure technique is used repeatedly, and the pricing formula is provided as the standard normal cumulative distribution functions.

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Pricing Vulnerable Options with Stochastic Volatility and Stochastic Interest Rate

Cited by 18 publications

References 27 publications

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

Valuation of Exchange Option with Credit Risk in a Hybrid Model

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