Shenghong Li

Pricing VXX option with default risk and positive volatility skew

This paper proposes and makes a comparative study of alternative models for VXX option pricing. Factors such as mean-reversion, jumps, default risk and positive volatility skew are taken into consideration. In particular, default risk is characterized by jump-to-default framework and the “positive volatility skew” issue is addressed by stochastic volatility of volatility and jumps. Daily calibration is conducted and comparative study of the models is performed to check whether they properly fit market prices and generate reasonable positive volatility skews and deltas. Overall, jump-to-default extended LRJ model with positive correlated stochastic volatility (called JDLRJSV in the paper) serves as the best model in all the required aspects.

A note on “Monte Carlo analysis of convertible bonds with reset clause” ☆

Kimura and Shinohara [T. Kimura, T. Shinohara, Monte Carlo analysis of convertible bonds with reset clauses, European Journal of Operational Research 168 (2006) 301-310] analyze the value of a non-callable convertible bond with a reset clause. For a reset convertible bond, the conversion ratio is not fixed but depends on the underlying stock price. However, their model does not consider a dilution effect which can result due to changes in the number of shares into which the bond is converted. In this paper, we have developed a new pricing formula for reset convertible bonds that adjusts for dilution.

Pricing model of interest rate swap with a bilateral default risk

Under the foundation of Duffie & Huang (1996) [7], this paper integrates the reduced form model and the structure model for a default risk measure, giving rise to a new pricing model of interest rate swap with a bilateral default risk. This model avoids the shortcomings of ignoring the dynamic movements of the firms assets of the reduced form model but adds only a little complexity and simplifies the pricing formula significantly when compared with Li (1998) [10]. With the help of the Crank-Nicholson difference method, we give the numerical solutions of the new model to study the default risk effects on the swap rate. We find that for a one year interest rate swap with the coupon paid per quarter, the variance of the default fixed rate payer decreases from 0.1 to 0.01 only causing about a 1.35%s increase in the swap rate. This is consistent with previous results.

The forward-path method for pricing multi-asset American-style options under general diffusion processes

The forward-path method is one of the effective memory reduction approaches in pricing multi-asset American-style options by the Monte Carlo simulation. However, when the underlying assets follow a general diffusion process, it would be difficult to apply this method. In this paper we propose a simple and effective method, which applies the Milstein-Taylor explicit and implicit schemes and makes it possible to apply the forward-path method under general diffusion processes. It preserves the advantage of high reduction with relatively low cost of the forward-path method. Moreover, it works as a plug-in and one can flexibly substitute the schemes with different ones for different problems. It is proven that our method can conveniently restore the simulated path with strong convergence order 1.0 . The numerical results indicate our method has high pricing accuracy and efficiency. Generalize the application of forward-path method to general diffusion model.Apply explicit and implicit Milstein-Taylor schemes to avoid solving equations.The method works as a plug-in with good flexibility.High accuracy in pricing American-style options by Least-Square Method.

Pricing Convertible Bond with Call Clause in Exponential Variance Gamma Model

In this paper, we get the pricing framework of the convertible bond (CB) with call clause in exponential variance gamma (EVG) model rather than the classical Black-Scholes (BS) model. From numerical calculation, we conclude that the new approach does lead to a different pricing method, but the difference of prices is insignificantly and the optimal stopping strategies are exactly the same.

Fast Greeks by simulation: The block adjoint method with memory reduction

The pathwise method is one of the approaches to calculate the option price sensitivities by Monte Carlo simulation. Under the general diffusion process, we usually use the Euler scheme to simulate the path of the underlying asset, which requires small time spaces to assure the convergence. The adjoint method can be used to accelerate the calculation of the Greeks in such case. However, it needs to store the intermediate information along the path. In this paper, we propose to use the block simulation to further accelerate the calculation. Block simulation can be seen as an extension of the common Monte Carlo simulation. It is simple to implement, without any extra work and loss in accuracy. It also has the flexibility on the block division, fitting to the computation environment. Moreover, we use the extended forward-path method along with the real time calculation strategy to do the memory reduction so that it can be combined with the adjoint method better. The numerical tests show our method can accelerate the adjoint method by several times. Our method is relatively even more efficient in the high-dimensional case.

Stochastic optimization based on principal-agent problem

By the theory of stochastic dynamic programming, we provide the methods for deriving the optimal rules. In this paper, we make two models in dynamic state process to maximize the expected utility of the agent and then obtain the famous Hamilton-Jacobi-Bellman equation. Furthermore, we derive explicit form solution and closed-form solution of the optimal equations for given utility functions.

Lundberg's Inequality of Erlang(2) Perturbed Risk Model in Markovian Environment

A famous problem in nonlife actuarial field is considered in this paper. We extend Erlang(2) perturbed risk model to a Markov dependent model in which the inter-claim time, the claim amount, the premium rate and the volatility of the diffusion process are all regulated by a continuous-time Markov process. By the means of the martingale approach, we obtain an upper bound of the ruin probability of our model, described as the Lundbergs inequality, and derive a representation for the corresponding adjustment coefficient.

Notice of Retraction The PIDE pricing model of interest rate swap with default risk under Variance Gamma process

In this paper, we intend to establish the PIDE pricing model of interest rate swap with default risk under Variance Gamma process. Under the assumption of the dynamics assets price process of a counterparty with Variance Gamma (VG) process, we treat the assets price process as a direct variable in the partial integro-differential equation (PIDE) of interest rate swap pricing, different from the working paper, in which they treat the default risk calculated from the Variance Gamma process as an item of the adjustment interest rate. At the end of this paper, we give a numerical result from the PIDE and find that a one hundred basis point of credit spread (bond spread) only results in 0.115 basis point in swap spread.

Pricing credit spread option with counterparty risk

In this paper, we have developed a pricing model for credit spread options with the existence of the counterparty default risk. The default dependence is modeled in the interacting intensities framework, and the correlation between default and the interest rate is considered. Semi-analytic pricing formulas for European credit spread put options with counterparty risk are derived. The numerical analysis shows that the counterparty default risk has a considerable influence on the value of a credit spread option.