Pricing of convertible bonds based on Normal Inverse Gaussian model

In the past few months, many stocks have experienced a decline in value with Chinese stock market exhibiting substantial volatility. And then, some related convertible bond prices repeatedly hit new lows. Therefore, when discussing convertible bond prices, it is often more realistic to impose an upper bound on underlying asset values. In this paper, we firstly derive the expression for the underlying asset price which follows exponential normal inverse Gaussian (NIG) process by Esscher transforms and the martingale measure method. Secondly, assuming that the underlying asset has an upper limit, we derive the analytical pricing formulas for convertible bonds which are expressed in the form of Fourier integrals. Finally, in the empirical section, using the maximum likelihood method to estimate the parameters in NIG process, we find that prices of the convertible bond derived from the NIG model are closest to the market prices than the Black-Scholes-Merton (BSM) and others.