Option pricing in Markov-modulated exponential Lévy models with stochastic interest rates

2019 ◽  
Vol 357 ◽  
pp. 146-160 ◽  
Author(s):  
Jiayong Bao ◽  
Yuexu Zhao
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
Exponential Lévy Models ◽  
Markov Modulated

scholarly journals Pricing Spread Options with Stochastic Interest Rates

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yunguo Jin ◽  
Shouming Zhong
Keyword(s):  
Option Pricing ◽  
Interest Rates ◽  
Stock Returns ◽  
Grid Method ◽  
Pricing Models ◽  
Stochastic Interest Rates ◽  
Spread Options ◽  
Asset Pricing Models ◽  
Stochastic Interest ◽  
Spread Option

Although spread options have been extensively studied in the literature, few papers deal with the problem of pricing spread options with stochastic interest rates. This study presents three novel spread option pricing models that permit the interest rates to be random. The paper not only presents a good approach to formulate spread option pricing models with stochastic interest rates but also offers a new test bed to understand the dynamics of option pricing with interest rates in a variety of asset pricing models. We discuss the merits of the models and techniques presented by us in some asset pricing models. Finally, we use regular grid method to the calculation of the formula when underlying stock returns are continuous and a mixture of both the regular grid method and a Monte Carlo method to the one when underlying stock returns are discontinuous, and sensitivity analyses are presented.

Changes of numéraire, changes of probability measure and option pricing

1995 ◽  
Vol 32 (02) ◽  
pp. 443-458 ◽  
Author(s):  
Hélyette Geman ◽  
Nicole El Karoui ◽  
Jean-Charles Rochet
Keyword(s):  
Probability Measure ◽  
Option Pricing ◽  
Interest Rates ◽  
Complete Markets ◽  
Stochastic Interest Rates ◽  
Stochastic Interest ◽  
Hedging Portfolio ◽  
Pricing Problems ◽  
Key Theorem ◽  
Efficient Selection

The use of the risk-neutral probability measure has proved to be very powerful for computing the prices of contingent claims in the context of complete markets, or the prices of redundant securities when the assumption of complete markets is relaxed. We show here that many other probability measures can be defined in the same way to solve different asset-pricing problems, in particular option pricing. Moreover, these probability measure changes are in fact associated with numéraire changes, this feature, besides providing a financial interpretation, permits efficient selection of the numéraire appropriate for the pricing of a given contingent claim and also permits exhibition of the hedging portfolio, which is in many respects more important than the valuation itself. The key theorem of general numéraire change is illustrated by many examples, among which the extension to a stochastic interest rates framework of the Margrabe formula, Geske formula, etc.

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