Pricing Perpetual American Put Options with Asset-Dependent Discounting

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

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A Shannon Wavelet Method for Pricing American Options under Two-Factor Stochastic Volatilities and Stochastic Interest Rate

Discrete Dynamics in Nature and Society ◽

10.1155/2020/8531959 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Huang Shoude ◽

Xunxiang Guo

Keyword(s):

Interest Rate ◽

Asset Price ◽

Heston Model ◽

Put Options ◽

American Put Options ◽

Stochastic Interest ◽

Stochastic Volatilities ◽

Shannon Wavelet ◽

Bermudan Options ◽

American Put

In the paper, the pricing of the American put options under the double Heston model with Cox–Ingersoll–Ross (CIR) interest rate process is studied. The characteristic function of the log asset price is derived, and thereby Bermuda options are well evaluated by means of a state-of-the-art Shannon wavelet inverse Fourier technique (SWIFT), which is a robust and highly efficient pricing method. Based on the SWIFT method, the price of American option can be approximated by using Richardson extrapolation schemes on a series of Bermudan options. Numerical experiments show that the proposed pricing method is efficient, especially for short-term American put options.

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Pricing of perpetual American put option with sub-mixed fractional Brownian motion

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2019-0060 ◽

2019 ◽

Vol 22 (4) ◽

pp. 1145-1154

Author(s):

Feng Xu ◽

Shengwu Zhou

Keyword(s):

Brownian Motion ◽

Fractional Brownian Motion ◽

Asset Price ◽

Put Options ◽

No Arbitrage ◽

American Put Option ◽

Put Option ◽

American Put Options ◽

Mixed Fractional Brownian Motion ◽

American Put

Abstract The pricing problem of perpetual American put options is investigated when the underlying asset price follows a sub-mixed fractional Brownian motion process. First of all, the sub-mixed fractional Black-Scholes partial differential equation is established by using the delta hedging method and the principle of no arbitrage. Then, by solving the free boundary problem, we get the pricing formula of the perpetual American put option.

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