Uncertainty and stochastic theories on European options valuation and their delta and vega risks

2022 ◽  
Author(s):  
Carlos Alexander Grajales ◽  
Santiago Medina Hurtado ◽  
Samuel A. Mongrut
Keyword(s):  
European Options ◽  
Options Valuation

A Review of Land Options Valuation

2019 ◽  
Vol 18 (3) ◽  
pp. 5-22
Author(s):  
Seung Dong You
Keyword(s):  
Options Valuation

THE FORWARD PDE FOR EUROPEAN OPTIONS ON STOCKS WITH FIXED FRACTIONAL JUMPS

2005 ◽  
Vol 08 (02) ◽  
pp. 239-253 ◽  
Author(s):  
PETER CARR ◽  
ALIREZA JAVAHERI
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Stock Price ◽  
Arrival Rate ◽  
European Options ◽  
Standard Assumption ◽  
Integro Differential Equation ◽  
Local Variance ◽  
Calendar Dates

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

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