New american option pricing model incorporates investor psychology and risk preferences
image: Our method for call options is summarised in the following algorithm: (1) We device the time interval into the grid 0≡t_0<t_1<...<t_n≡T and let D_0,D_1...,D_n be some values for the underlying asset at these nodes. We shall approximate the optimal boundary maximizing the holder’s financial result at this grid deriving the appropriate values of D’s. (2) We use the closed-form formula for the price of a European-style option that expires when the underlying asset reaches an exponent of the piecewise linear function that relates the values D_0,D_1...,D_nat the grid–see Formula (3.21). We denote this price by V(x;{t_0,...,t_n};{D_0,...,D_n}). (3) The optimal boundary at the maturity D_n is given by Formula (2.14). (4) Suppose that we know the values of the optimal boundary at the moments t_m,t_(m+1)…,t_n – we denote them by D_m,D_(m+1)…,D_n – for some m<n. For a fixed value x of the asset price at the previous moment t_(m-1), we defined d(x) as the value for the boundary that maximizes the holder’s financial result: d(x)=argmax{D:V(x;{0,t_m-t_(m-1)...,t_nt_(m-1)};{D,D_m,...,D_n })}. (2.18) (5) We approximate the value of the optimal boundary at the previous time-node t_(m-1) as D_(m-1)=min{x:D(x)=x}. In fact, this is the lower value for which the immediate exercise is optimal.
Credit: Tsvetelin Zaevski.
Background and Motivation
Traditional American option pricing models assume rational investors exercise options only when the underlying asset hits an optimal boundary. However, real-world investors often make decisions based on psychological factors and risk preferences that deviate from theoretical optima. This research addresses this gap by developing a more realistic pricing framework that accounts for investors' tendency to exercise options within an "ϵ-optimal set" beyond the conventional boundary.
Methodology and Scope
The study examines both put and call options separately under a novel framework where exercise occurs not only at the optimal boundary but also within a properly defined ϵ-optimal set. For perpetual possibilities, the research derives closed-form analytical formulas. For finite-maturity options, the study constructs a numerical algorithm to approximate the ϵ-optimal strip and adapts the Crank-Nicolson finite difference method to compute option prices, specifically identifying the price interval within which the value varies.
Key Findings and Contributions
The research successfully derives closed-form pricing formulas for perpetual American options under the ϵ-optimal exercise assumption. For finite-maturity options, it develops a robust numerical algorithm that effectively approximates the ϵ-optimal exercise strip and determines precise price intervals. The study represents a significant advancement in option pricing theory by formally incorporating investor risk preferences into the framework for exercising options.
Why It Matters
This research bridges an important gap between theoretical finance and behavioural economics by acknowledging that investors don't always behave as perfectly rational agents. By incorporating psychological factors and risk preferences into the pricing model, the study provides a more accurate representation of real market behaviour, offering both theoretical insights and practical tools for financial professionals.
Practical Applications
- Financial institutions can utilise this model for more accurate risk assessment of American-style derivatives.
- Option traders can better understand price intervals when the underlying asset approaches critical levels.
- Risk managers can incorporate ϵ-optimal exercise behaviour into their hedging strategies.
- Academic researchers can build upon this framework to develop more behaviorally realistic financial models
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