Abstract
In this study, we propose an equilibrium pricing rule to capture a characteristic observed in the practical option market. The market has observed that the implied volatility derived from the Black-Scholes formula is monotonically decreasing with the strike price for the option, that is, it exhibits volatility skewness. Here, we construct a pricing method for the so-called economic premium principle. That is, we identify a pricing kernel from which we can evaluate the derivative from the market equilibrium. Our model demonstrates how to obtain a pricing kernel that satisfies the market equilibrium, and describes our equilibrium formula depicting the volatility skewness.
Highlights
In this study, we consider an option product written on stock, and propose an equilibrium pricing rule to capture a characteristic observed in the practical option market
We propose an equilibrium pricing rule to capture a characteristic observed in the practical option market
We identify a pricing kernel from which we can evaluate the derivative from the market equilibrium
Summary
We consider an option product written on stock, and propose an equilibrium pricing rule to capture a characteristic observed in the practical option market. Yamazaki [10] does not explain the theory of how the change in consumption is modeled by the stock return and its volatility; that is, it remains exogenous Another approach used to determine the pricing kernel is that of Bühlmann [12]. This property is independent of whether we consider the stochastic volatility This means that the pricing kernel derived from risk-averse investors produces the volatility skewness. With π h i denoting the money amount invested in the risky asset i by investor h ∈ buy sell and kh (≥ 0) the position of the option, the money amount ml deposited into the bank account by buyer l is.
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