An optimal stochastic control framework for determining the cost of hedging of variable annuities

An implicit partial differential equation (PDE) method is used to determine the cost of hedging for a Guaranteed Lifelong Withdrawal Benefit (GLWB) variable annuity contract. In the basic setting, the underlying risky asset is assumed to evolve according to geometric Brownian motion, but this is generalised to the case of a Markov regime switching process. A similarity transformation is used to reduce a pricing problem with K regimes to the solution of K coupled one dimensional PDEs, resulting in a considerable gain in computational efficiency. The methodology developed is flexible in the sense that it can calculate the cost of hedging for a variety of different withdrawal strategies by investors. Cases considered here include both optimal withdrawal strategies (i.e. strategies which generate the highest possible cost of hedging for the insurer) and sub-optimal withdrawal strategies in which the policy holder׳s decisions depend on the moneyness of the embedded options. Numerical results are presented which demonstrate the sensitivity of the cost of hedging (given the withdrawal specification) to various economic and contractual assumptions.     

Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate

Decisions in Economics and Finance - In this paper, we investigate value and Greeks computation of a guaranteed minimum withdrawal benefit (GMWB) variable annuity, when both stochastic volatility...     

Jump dynamics,spillover effect and option valuation

In this paper, we propose an affine discrete-time model that incorporates the jump process and spillover effect for valuing the 50 ETF options in China. Based on the proposed model, a closed-form solution is also derived for the new dynamics of underlying asset, which facilitates option pricing. The empirical results show that the proposed model offers greater economic benefit with reduced pricing errors than the traditional benchmark models, including the popular HNGARCH model of Heston and Nandi (2000), GARV model of Christoffersen et al. (2014), and BPJVM model of Christoffersen et al. (2015). Our finding is important for financial risk management and investment in Chinese derivatives market.     

Dupire’s formulas in the Piterbarg option pricing model

In this paper we derive an expression for the local volatility of an underlying asset, given the prices of liquid European call options under the Piterbarg framework. The Piterbarg framework is a multi-curve derivative pricing model which extends the well known Black–Scholes–Merton model by relaxing the assumption of a risk-free interest rate, and includes collateral payments. The expressions for the local volatility is a function of the option price surface, and is then transformed to become a function of the implied volatility surface.     

Using a decision tree to analyze mortgage borrower decision behavior and values concerning interest rates and house prices

In reality, mortgage borrowers are more seriously concerned with the current mortgage boundary (i.e. option exercise) value than with the current option value (i.e. expected present value of the prospective option exercise value). Hence, by combining a simulation framework and a decision tree, the terminations of mortgage behavior can be classified forward but not backward as by the binomial lattice. After simulating 5000 projections for both Taiwan house prices and interest rates, as well as computing for current mortgage boundary values obtained by modifying Ambrose and Buttimer ( 2000 ) to step through the mortgage decision tree, the result shows that the prepayment is affected by rising interest rate volatility. Moreover, the delinquency and the reinstatement are affected by both rising interest rate and house price volatilities. However, due to the cost of delinquency and credit penalties, the foreclosure could not compete over the reinstatement when house prices and interest rates are in a high‐volatility situation. The reinstatement is encouraging for the borrowers. Copyright © 2010 John Wiley & Sons, Ltd.     

From agent-based modeling to actor-based reactive systems in the analysis of financial networks

We present a new framework for the analysis of financial networks, called Actor-based Reactive Systems (ARS), that pushes further the Agent-Based approach (ABM) by resorting to ideas coming from the study of distributed systems in computer science. Two distinctive features, namely a fundamentally different management of time and a fully decentralized control logic, have a profound impact in terms of expressiveness of analysis, flexibility of modeling, and efficiency of experimentation. To illustrate the feasibility of the framework, we develop a realistic case study by analyzing the systemic risk of a model of the European banking network with a nontrivial contagion procedure, that combines an initial asset shock with the negative feedback loop triggered by asset fire sales. We show that, compared to ABMs, ARSs bring about finer-grained analyses, with a greater degree of heterogeneity and adaptivity of economic agents. Moreover, the very low computational cost and the detailed account of the system’s execution support the design and the development of very flexible stress tests to rapidly experiment with many hypothetical scenarios in a test-oriented style.

     

Valuation of double trigger catastrophe options with counterparty risk

This study presents a novel catastrophe option pricing model that considers counterparty risk. Asset prices are modeled through a jump-diffusion process which is correlated to counterparty loss process and collateral assets. Because of the long term of catastrophe options, this study also examines the model in the stochastic interest rate environment. The numerical results indicate that counterparty risk significantly affects the value of options. Recently, numerous serious financial events have demonstrated the importance of counterparty risk when valuing financial products.     

Pricing perpetual options with stochastic discount interest rates

The aim of this study is to investigate the prices and optimal exercise strategies of certain perpetual American options on the asset under stochastic discount interest model. This is different from Gerber and Shiu (N Am Actuar J 2(3):101–112, 1998), in which the interest force was a constant; here we suppose that the accumulated interest function is perturbed by the standard Brownian motion and Poisson process. We obtain an explicit expression of optimal option-exercise boundary in the case of perpetual put option. Moreover, we get a corresponding result when the individual claim is described by an exponential distribution. Finally, we analyze the influence of certain coefficients in stochastic interest model on the optimal option-exercise boundary.     

European quanto option pricing in presence of liquidity risk

In this paper, we study the pricing problems of the European quanto options in which the underlying foreign asset is in imperfectly liquid markets. First, we assume that the dynamics of the underlying foreign asset price are affected by market liquidity and propose a liquidity-adjusted quanto model. This allows for the effects of market liquidity on European quanto option pricing. And then we derive the analytical pricing formulas for four different types of European quanto options. Finally, we empirically investigate the pricing performance of our proposed model with a European quanto construction involving the SSE 50 ETF, as the underlying asset, and the CNY/HKD exchange rate. Empirical results demonstrate that the pricing accuracy of the proposed model is markedly superior to that of the Black-Scholes quanto model. In other words, allowing for liquidity risk in the framework of European quanto option pricing can make markedly improvements in fitting the real market data. Particularly, the improvement rate is high for medium-term and out-of-the-money options. Moreover, these results are robust for different liquidity measures.     

Innovation dynamics and fiscal policy: Implications for growth,asset prices,and welfare

We study the equilibrium implications of different fiscal policies on macroeconomic quantities and welfare by utilizing an endogenous growth model that matches asset pricing data well. The fiscal instruments of interest are (i) subsidies to R&D expenditure, consumption and capital investment, and (ii) cuts in labor and corporate tax rates. Our equilibrium analysis provides new insights on the interplay of innovation dynamics and fiscal policy. Importantly, we find growth and welfare to be inversely related when changing R&D subsidies. However, this depends on how well the model reproduces asset pricing dynamics. Moreover, only subsidies to capital investments and cuts in the corporate tax rate have the potential to increase both growth and welfare.     

Fluctuating uncertainty and flexibility value

A simple model of recurrent fluctuating uncertainty with two types of investment assets, commitment and flexible, where fluctuating uncertainty is defined as changes between high and low confidence regimes, is constructed. By assuming risk neutrality, I find analytically a formula for flexibility value that is defined as the difference between the expected return to the commitment asset and the expected return to the flexible asset. This flexibility value is positive in the low confidence regime because of a positive attribute of the flexibility asset that is the option to utilize new information later. The relation between flexibility value and other parameters of the model is also considered. Flexibility value increases as the information an individual obtains in the high confidence regime increases or the discounting factor of the individual increases. Finally, flexibility value can increase even if, ceteris paribus, the return to the commitment asset increases.     

From constrained optimization to constrained dynamics: extending analogies between economics and mechanics

Economic equilibrium models have been inspired by analogies to stationary states in classical mechanics. To extend these mathematical analogies from constrained optimization to constrained dynamics, we formalize economic (constraint) forces and economic power in analogy to physical (constraint) forces and the reciprocal value of mass. Agents employ forces to change economic variables according to their desire and their power to assert their interest. These ex-ante forces are completed by constraint forces from unanticipated system constraints to yield the ex-post dynamics. The differential-algebraic equation framework seeks to overcome some restrictions inherent to the optimization approach and to provide an out-of-equilibrium foundation for general equilibrium models. We transform a static Edgeworth box exchange model into a dynamic model with procedural rationality (gradient climbing) and slow price adaptation, and discuss advantages, caveats, and possible extensions of the modeling framework.

     

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump-diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.     

基于实物期权法的风险投资项目估价方法——一个文献综述

本文理清了实物期权及其在风险投资项目估价中应用的发展脉络,并提出了实物期权在风险投资项目估价应用中需要发展的地方。     

Prospect Theory in the Heterogeneous Agent Model

Using the Heterogeneous Agent Model framework, we incorporate an extension based on Prospect Theory into a popular agent-based asset pricing model. This extension covers the phenomenon of loss aversion manifested in risk aversion and asymmetric treatment of gains and losses. Using Monte Carlo methods, we investigate behavior and statistical properties of the extended model and assess how our extension is manifested in different strategies. We show that, on the one hand, the Prospect Theory extension keeps the essential underlying mechanics of the model intact, but on the other hand it considerably changes the model dynamics. Stability of the model is increased and fundamentalists may be able to survive in the market more easily. When only the fundamentalists are loss-averse, other strategies profit more.

     

MODELLING REGIME SWITCHING AND STRUCTURAL BREAKS WITH AN INFINITE HIDDEN MARKOV MODEL

This paper proposes an infinite hidden Markov model to integrate the regime switching and structural break dynamics in a unified Bayesian framework. Two parallel hierarchical structures, one governing the transition probabilities and another governing the parameters of the conditional data density, keep the model parsimonious and improve forecasts. This flexible approach allows for regime persistence and estimates the number of states automatically. An application to US real interest rates compares the new model to existing parametric alternatives. Copyright © 2013 John Wiley & Sons, Ltd.     

Joint dynamic modeling and option pricing in incomplete derivative-security market

In this study, we evaluate the option prices on two assets under stochastic interest rates when the stochastic process that underlying asset prices follow is depending on a correlated bivariate Markov-modulated geometric Brownian motion model with jump risks. More specifically, we conduct the joint dynamic modeling by identifying two independent compound Poisson processes with the log-normal jump sizes to describe both individual jumps and systematic cojumps. Facilitating the cojumping behavior this way with the time-inhomogeneity of the volatility, option pricing expressions are readily obtainable since the Gerber–Siu’s approach is employed to determine a pricing kernel. The empirical results and numerical illustrations are provided to show the impact of cojumps and stochastic volatilities on option prices.     

Asset price dynamics with heterogeneous beliefs and local network interactions

In this paper we investigate the effects of network topologies on asset price dynamics. We introduce network communications into a simple asset pricing model with heterogeneous beliefs. The agents may switch between several belief types according to their performance. The performance information is available to the agents only locally through their own experience and the experience of other agents directly connected to them. We model the communications with four commonly considered network topologies: a fully connected network, a regular lattice, a small world, and a random graph. The results show that the network topologies influence asset price dynamics in terms of the regions of stability, amplitudes of fluctuations and statistical properties.     

Evaluation of American option prices in a path integral framework using Fourier–Hermite series expansions

In this paper we review the path integral technique which has wide applications in statistical physics and relate it to the backward recursion technique which is widely used for the evaluation of derivative securities. We formulate the pricing of equity options, both European and American, using the path integral framework. Discretising in the time variable and using expansions in Fourier–Hermite series for the continuous representation of the underlying asset price, we show how these options can be evaluated in the path integral framework. For American options, the solution technique facilitates the accurate determination of the early exercise boundary as part of the solution. Additionally, the continuous representation of the state variable allows the relatively accurate and efficient evaluation of the option prices and the delta hedge ratio.     

Impact of investor’s varying risk aversion on the dynamics of asset price fluctuations

While investors’ responses to price changes and their price forecast have been identified as one of the major factors contributing to large price fluctuations in financial markets, our study shows that investors’ heterogeneous and dynamic risk aversion (DRA) preferences may play a more critical role in understanding the dynamics of asset price fluctuations. We allow an agent specific and time-dependent risk aversion index in a popular power utility function with constant relative risk aversion to construct our DRA model in which we made two key contributions. We developed an approximated closed-form price setting equation, providing a necessary framework for exploring the impact of various agents’ behaviors on the price dynamics. The dynamics of each agent’s risk aversion index is modeled by a bounded random walk with a constant variance, and such dynamics is incorporated in the price formula to form our DRA model. We show numerically that our model reproduces most of the “stylized” facts observed in the real data, suggesting that dynamic risk aversion is an important mechanism for understanding the dynamics of the financial market and the resultant financial time series.