First Passage Time for Tempered Stable Process and Its Application to Perpetual American Option and Barrier Option Pricing

TL;DR

This paper derives an explicit or numerical approximation of the first passage time for tempered stable processes and applies it to pricing perpetual American and barrier options, supported by numerical calibration to market data.

Contribution

It introduces a new method to approximate the first passage time characteristic function for tempered stable processes and applies it to option pricing.

Findings

Explicit and numerical characteristic functions are provided.

The method is calibrated to market call and put prices.

Numerical results demonstrate the approach's effectiveness.

Abstract

In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process is provided explicitly or by an indirect numerical method. This will be applied to the perpetual American option pricing and the barrier option pricing. Numerical illustrations are provided for the calibrated parameters using the market call and put prices.