# Stochastic interest rate option pricing

Suppose that the interest rates obey stochastic differential equations, while the exchange rate follows an uncertain differential equation; this paper proposes a new currency model. Under the proposed currency model, the pricing formula of European currency options is then derived. Some numerical examples recorded illustrate the quality of pricing formulas. Meanwhile, this paper analyzes the I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are nonrandom, i.e. known): Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing Peter Carr Bloomberg LP and Courant Institute, New York University Xavier Gabaix Stern School of Business, New York University Liuren Wu Zicklin School of Business, Baruch College, CUNY ABSTRACT Secondly, the paper extends the COS method to forward starting options pricing with stochastic interest rates. The rest of the paper is organized as follows. Section 2 develops the underlying pricing model. Section 3 derives the characteristic function and forward characteristic function of the log asset price. The challenge in pricing spread options stems from the fact that there is no explicit solution. Furthermore, the pricing of options with stochastic interest rates can generally be difficult. Therefore, pricing spread options with stochastic interest rates is a challenging task in finance and is important for both theory and applications. Theorem 5.

## In this paper, we consider the problem of pricing European options, namely vanilla options, binary options and exchange options, whose underlying assets prices dynamics follow Markovian regime switching exponential Lévy models with stochastic interest rates, where the stochastic interest rates are driven by Markovian regime switching Hull–White process.

Abstract: This paper reviews the option pricing model and its application, on the basis of former studies, we assume that the interest rate satisfy a given Vasicek  Section 2 outlines a spread option pricing model with stochastic interest rates and presents a technique of measure changes to the price of the spread option.

### The challenge in pricing spread options stems from the fact that there is no explicit solution. Furthermore, the pricing of options with stochastic interest rates can generally be difficult. Therefore, pricing spread options with stochastic interest rates is a challenging task in finance and is important for both theory and applications. Theorem 5.

Incorporating stochastic interest rate into stock option pricing model is another line of extension. At the earliest Merton (1973) has discussed option pricing under  We will generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literature has obtained some. Abstract: This paper reviews the option pricing model and its application, on the basis of former studies, we assume that the interest rate satisfy a given Vasicek  Section 2 outlines a spread option pricing model with stochastic interest rates and presents a technique of measure changes to the price of the spread option. This work deals with European option pricing problem in fractional Brownian markets. Two factors, stochastic interest rates and transaction costs, are taken into  A short-rate model, in the context of interest rate derivatives, is a mathematical model that Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. short rate tree or simulation; see Lattice model ( finance)#Interest rate derivatives and Monte Carlo methods for option pricing.

### problem under both stochastic volatility and stochastic interest rates, but some The price of an American compound option under stochastic volatility at time t,

Abstract. This paper develops a general valuation approach to price barrier options when the term structure of interest rates is stochastic. These products'

## FORWARD START OPTIONS UNDER STOCHASTIC VOLATILITY AND with the CIR (Econometrica53 (1985) 385–408) stochastic interest rates. The main result is an analytic formula for the price of a forward start European call option.

We present a European option pricing when the underlying asset price dynamics is governed by a linear combination of the time-change Lévy process and a stochastic interest rate which follows the Vasicek process. We obtain an explicit formula for the European call option in term of the characteristic function of the tail probabilities. The Call Option Pricing Based on Investment Strategy with Stochastic Interest Rate Article (PDF Available) in Journal of Mathematical Finance 08(01):43-57 · January 2018 with 141 Reads the entire evolution of interest rates and a continuum of bonds. This paper’s contribution is to provide an alternative class of option pricing models which incorporate stochastic interest rates yet avoid the shortcomings of Merton’s formulation. This approach is based on the martingale measure In this paper, we consider the problem of pricing European options, namely vanilla options, binary options and exchange options, whose underlying assets prices dynamics follow Markovian regime switching exponential Lévy models with stochastic interest rates, where the stochastic interest rates are driven by Markovian regime switching Hull–White process. I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are nonrandom, i.e. known):

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