Generic pricing of foreign exchange, inflation and stock options under stochastic interest rates and stochastic volatility

In this paper we deal with the pricing of stock, foreign exchange and inflation options under stochastic interest rates and stochastic volatility. We consider a foreign exchange framework for the pricing inflation-indexed options in which the valuation of stock and foreign exchange options can be treated as a nested case. We assume multi-factor Gaussian rates for both the nominal (domestic) as the real (foreign) economy, which economies (currencies) can be exchanged against each other by means of the inflation index (exchange rate) which is driven by log-normal dynamics with a stochastic volatility component. Furthermore we allow for a general correlation structurebetween the drivers of the volatility, the inflation index, the nominal and the real rates. We derive explicit option pricing formulas for various securities, like vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. All these options can be valued in closed-form under Schöbel-Zhu (1999) stochastic volatility, whereas we device an (Monte Carlo) approximation in the form of a very e ective control variate for the general Heston (1993) model.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.

MORE ABOUT NETSPAR


Mission en strategy           •           Network           •           Organisation           •          Magazine
Netspar Brief            •            Actionplan 2019-2023           •           Researchagenda

ABOUT NETSPAR

Our partners

B20220412_SPIN_logo+naam_2xPMS_2_voettekst
B20160708_universiteit leiden
B20160708_asr
BPL_Pensioen_logo+pay-off - 1610-1225 v1.1_grijswaarden
B20220329_sph huisartsen
View all partners