A Parsimonious Model for Intraday European Option Pricing

Abstract

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Limit theorems for prices of options written on semi-Markov processes

“…The main difference with the present paper is that the authors of [30] assumed that, at time t, the investor just knows the number of trades since the beginning of continuous trading whereas here, as in Montero's case, we assume full knowledge of the past history of the process including the age, that is the time passed from the instant of the previous trade assumed as a renewal point. If the age is known, the history of the process before the previous renewal is not relevant, leading to a simplification of (III.1).…”

“…The result we prove in Theorem 1 is strictly related to this work. Scalas and Politi [30] considered the very same model discussed below and presented the explicit formula for the option price given here in equation (III.1).…”

Limit theorems for prices of options written on semi-Markov processes

“…Scalas and Politi [30] considered the very same model discussed below and presented the explicit formula for the option price given here in equation (3.3). The main difference with the present paper is that the authors of [30] assumed that, at time t, the investor just knows the number of trades since the beginning of continuous trading whereas here, as in Montero's case, we assume full knowledge of the past history of the process including the age, that is the time passed from the instant of the previous trade assumed as a renewal point. If the age is known, the history of the process before the previous renewal is not relevant, leading to a simplification of (3.3).…”