A full asymptotic series of European call option prices in the SABR model with beta=1

<p>We develop two pricing formulae for European options in the SABR model with beta= 1 case by means of Malliavin Calculus. We follow the approach of Alòs et al (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term, by using the conditional density of the average volatility, and write it as a two-dimensional integral. For the correction part, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin, Peng, and Schellhorn (2016) with analytical calculations. The first approach, which we call "Dyson series on the return's idiosyncratic noise" yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor's (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion.The second approach, which we call "Dyson series on the common noise" necessitates the calculation of only a one-dimensional integral, but the formula is more complex.</p>

Name thesis:degree_name

Mathematics, PhD

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Institute of Mathematical Sciences

Year dc:date.available

2019

Author dc:creator

• Guo, Zhengji

Contributors dc:contributor

• John Angus
• Qidi Peng

• Exponential formula
• Malliavin Calculus
• option pricing
• SABR model
• stochastic volatility

Repository record dc:identifier

https://scholarship.claremont.edu/cgu_etd/510

OAI identifier oai:identifier

oai:scholarship.claremont.edu:cgu_etd-1450