scholarly journals Pricing and hedging bond options and sinking-fund bonds under the CIR model

2022 ◽  
Vol 6 (1) ◽  
pp. 1-34
Author(s):  
Manuela Larguinho ◽  
◽  
José Carlos Dias ◽  
Carlos A. Braumann ◽  
◽  
...  
Keyword(s):  
Interest Rate ◽  
Static Properties ◽  
Cir Model ◽  
Closed Form Solutions ◽  
Static Hedging ◽  
Hedging Portfolio ◽  
Bond Options ◽  
Portfolio Approach ◽  
Interest Rate Model ◽  
Coupon Bond

<abstract><p>This article derives simple closed-form solutions for computing Greeks of zero-coupon and coupon-bearing bond options under the CIR interest rate model, which are shown to be accurate, easy to implement, and computationally highly efficient. These novel analytical solutions allow us to extend the literature in two other directions. First, the static hedging portfolio approach is used for pricing and hedging American-style plain-vanilla zero-coupon bond options under the CIR model. Second, we derive analytically the comparative static properties of sinking-fund bonds under the same interest rate modeling setup.</p></abstract>

scholarly journals Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Guoan Huang ◽  
Guohe Deng ◽  
Lihong Huang
Keyword(s):  
Interest Rate ◽  
Optimal Stopping ◽  
Factor Model ◽  
Integral Representations ◽  
Quadrature Formulas ◽  
Short Term ◽  
Put Option ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Coupon Bond

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim's equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optimal stopping and exercise boundaries by quadrature formulas. Numerical results and discussions are provided.

Exponential ergodicity of CIR interest rate model with random switching

2016 ◽  
Vol 17 (05) ◽  
pp. 1750037 ◽  
Author(s):  
Jinying Tong ◽  
Zhenzhong Zhang
Keyword(s):  
Interest Rate ◽  
Stationary Distribution ◽  
Wasserstein Distance ◽  
Transition Semigroup ◽  
Rate Model ◽  
Cir Model ◽  
Exponential Ergodicity ◽  
The Central Limit Theorem ◽  
Random Switching ◽  
Interest Rate Model

In this paper, we consider ergodicity of Cox–Ingersoll–Ross (CIR) interest rate model with random switching. First, we show that the CIR model with switching has a unique stationary distribution. Next, we prove that the transition semigroup for the CIR model with switching converges to the stationary distribution at an exponential rate in the Wasserstein distance. Moreover, under two particular cases, the explicit expressions for stationary distributions are presented. Finally, the central limit theorem for the CIR model with random switching is established.

Valuing and Analyzing Fixed Income Derivatives

2019 ◽  
pp. 501-520
Author(s):  
Koray D. Simsek ◽  
Halil Kiymaz
Keyword(s):  
Interest Rate ◽  
Forward Rate ◽  
Fixed Income ◽  
Closed Form Solutions ◽  
Fixed Income Derivatives ◽  
Treasury Bond ◽  
Bond Options ◽  
Cost Of Carry ◽  
Risk Free Rate ◽  
Traditional Approaches

Derivatives valuation is based on the key principle of no-arbitrage pricing. This chapter presents valuation models for various types of fixed income derivatives, including forward rate agreements (FRAs), interest rate swaps, Eurodollar and Treasury bond futures, bond options, caps and floors, swaptions, and options on interest rate futures. Following the financial crisis that began in the summer of 2007, major changes occurred in the practice of fixed income derivatives valuation, particularly regarding the adoption of overnight indexed swaps (OIS) as a source of the risk-free rate. This chapter shows how OIS discounting is implemented in FRA pricing and swap valuation. Traditional approaches such as cost of carry valuation in futures pricing are illustrated. With respect to option valuation, this chapter explains the risk-neutral pricing approach as well as closed-form solutions such as the Black model. The chapter also provides numeric examples to illustrate the practical use of the presented models and formulas.

scholarly journals Lévy Interest Rate Models with a Long Memory

Risks ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Donatien Hainaut
Keyword(s):  
Interest Rate ◽  
Long Memory ◽  
Sample Path ◽  
Rate Model ◽  
Short Term ◽  
Uhlenbeck Process ◽  
Interest Rate Models ◽  
Infinite Dimensional ◽  
Bond Options ◽  
Interest Rate Model

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform.

scholarly journals HOLDER-EXTENDIBLE EUROPEAN OPTION: CORRECTIONS AND EXTENSIONS

2015 ◽  
Vol 56 (4) ◽  
pp. 359-372 ◽  
Author(s):  
PAVEL V. SHEVCHENKO
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Real Life ◽  
Option Price ◽  
Geometric Brownian Motion ◽  
Fixed Amount ◽  
Underlying Asset ◽  
Closed Form Solutions ◽  
Pricing Options ◽  
Interest Rate Volatility

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.

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