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

<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>

Bond and Option Prices under Skew Vasicek Model with Transaction Cost

This paper studies the European option pricing on the zero-coupon bond in which the Skew Vasicek model uses to predict the interest rate amount. To do this, we apply the skew Brownian motion as the random part of the model and show that results of the model predictions are better than other types of the model. Besides, we obtain an analytical formula for pricing the zero-coupon bond and find the European option price by constructing a portfolio that contains the option and a share of the bond. Since the skew Brownian motion is not a martingale, thus we add transaction costs to the portfolio, where the time between trades follows the exponential distribution. Finally, some numerical results are presented to show the efficiency of the proposed model.

Zero-Coupon Yields and the Cross-Section of Bond Prices

I estimate a dynamic term structure model on an unbalanced panel of Treasury coupon bonds, without relying on an interpolated zero-coupon yield curve. A linearity-generating model, which separates the parameters that govern the cross-sectional and time-series moments of the model, takes about 8 min to estimate on a sample of over 1 million bond prices. The traditional exponential affine model takes about 2 hr, because of a convexity term in coupon-bond prices that cannot be concentrated out of the cross-sectional likelihood. I quantify the on-the-run premium and a “notes versus bonds” premium from 1990 to 2017 in a single, easy-to-estimate no-arbitrage model.

Valuasi One Period Coupon Bond dengan Aset Mengikuti Model Geometric Brownian Motion with Jump Diffusion

<p>One period coupon bond gives coupon once a bond life together with the principal debt. If the firm’s asset value on maturity date is insufficient to meet the debtholder’s claim, then the firm is stated as default. The well-known model for predicting default probability is KMV-Merton model. Under this model, it is assumed that the return on the firm’s assets is distributed normally and their behaviour can be described with the Geometric Brownian Motion (GBM) formula. In practice, most of the financial data tend to have heavy-tailed distribution. It indicates that the data contain some extreme values. GBM with Jump is a popular model to capture the extreme values. In this paper, we evaluate a corporate bond which has some extreme condition in their asset value and predicts the default probability in the maturity date. Empirical studies were carried out on bond that is issued by CIMB Niaga Bank that has a payment due in November 2020. The result shows that modelling the asset value is more appropriate by using GBM with Jump rather than GBM modelling. Estimation to CIMB Niaga Bank equity in November 2020 is IDR 246,533,573,844,229.00. The liability of this company is IDR 4,205,751,155,771.00. The prediction of CIMB Niaga Bank default probability is 1.065812 ´ 10^-8 at the bond maturity. It indicates that the company is considered capable of fulfilling the obligations at the maturity date.</p><p><strong>Keywords: </strong>jump diffusion, extreme value, probability default, equity, liability</p>

Evaluation of Equity-linked structured products and pricing

Based on a unique data set, this research paper examines the pricing of equity-linked structured products in the market. The following section of this paper look at examining a few popular products available in the market, describing their key characteristics, and identifying one such product which will be examined closely for the purposes of determining if the issuing institution has priced the same fairly. The daily closing prices of a large variety of structured products are compared to theoretical values derived from the prices of options traded on the Eurex (European Exchange). This research paper also provides a brief background on the pricing of equity-linked structured products (‘products’) and issues around valuation of these products and look in detail fair pricing of the zero-coupon bond and the basket option. Comparing this with the market price of the instrument I could draw conclusions based on how close the real market price of the instrument is with the recomputed price.

Coupon Bond Duration and Convexity Analysis

Coupon bond duration and convexity are the primary risk measures for bonds. Given their importance, there is abundant literature covering their analysis, with calculus being used as the dominant approach. On the other hand, some authors have treated coupon bond duration and convexity without the use of differential calculus. However, none of them provided a complete analysis of bond duration and convexity properties. Therefore, this chapter fills in the gap. Since the application of calculus may be complicated or even inappropriate if the functions in question are not differentiable (as indeed is the case with the bond duration and convexity functions), in this chapter the properties of bond duration and convexity functions by using elementary algebra only are proved. This provides an easier way of approaching this problem, thus making it accessible to a wider audience not necessarily familiar with tools of mathematical analysis. Finally, the properties of these functions are illustrated by using empirical data on coupon bonds.

The Pricing of Double Trigger Catastrophe Put Option with Default Risk

This study was present a catastrophe put option pricing model that considers default risk. The default of the option issuer can occur at any time before the maturity, and there is a correlation between the total assets of the option issuer, the underlying stock and the zero coupon bond. The explicit solution of option pricing is obtained when the interest rate process follows the Vasicek model and relevant proofs are given. Finally, the value changes under different parameters are discussed through a numerical analysis.