Pricing vulnerable options with jump risk and liquidity risk

Review of Derivatives Research - In this paper, we consider vulnerable options with jump risk and liquidity risk. In the proposed framework, we allow discontinuous changes in the information...     

Pricing of swaps with default risk

In this paper, I study the valuation of interest rate and currency swaps with default risk under the contingent claim analysis framework. I demonstrate that the traditional approach of pricing swap contracts as exchanges of loans underestimates the value of such contracts to the counterparty with higher credit rating and exaggerates the credit spread required to guard against default risk. Numerical simulations show that the swap rate is not sensitive to counterparty credit rating: for a ten year interest rate swap, a one hundred basis point increase in counterparty bond yield spread results in only about one basis point increase in the swap rate. (JEL G10, G12, G13)This paper is based on Chapter 2 of my Ph.D. dissertation at Yale University. I would like to thank my dissertation committee, Kenneth French, Roger Ibbotson, and Jonathan Ingersoll, Jr. (chairman), for helpful advice and guidance. I would also like to thank Keny Back, Richard Lindsey, N. R. Prabhala, Ming Huang, Marti Subrahmanyam, three anonymous referees and especially Bob Jarrow, the editor, for helpful comments and suggestions. Any errors that remain are solely mine. This paper won the 1996 Trefftzs Award for best student paper from the Western Finance Association.     

Pricing inflation-indexed derivatives with default risk

Inflation-indexed derivatives with default risk are modeled using the jump-diffusion processes in the Heath–Jarrow–Morton’s (HJM) [(1992). “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claim Valuation.” Econometrica 60: 77–105] framework. A four-factor HJM model is proposed by incorporating an exogenous intensity function into a foreign currency analogy under the three-factor HJM model proposed by Jarrow and Yildirim [(2003). “Pricing Treasury Inflation Protected Securities and Related Derivatives Using a HJM Model.” Journal of Financial and Quantitative Analysis 38: 337–358]. The proposed model improves the valuation accuracy of zero-coupon inflation-indexed swaps (IIS) through calibrating the model to swap market data. In addition, the valuation formulas of year-on-year IIS and caps with default risk are derived.     

Pricing jump risk with utility indifference

This paper is concerned with option pricing in an incomplete market driven by a jump-diffusion process. We price options according to the principle of utility indifference. Our main contribution is an efficient multi-nomial tree method for computing the utility indifference prices for both European and American options. Moreover, we conduct an extensive numerical study to examine how the indifference prices vary in response to changes in the major model parameters. It is shown that the model reproduces ‘crash-o-phobia’ and other features of market prices of options. In addition, we find that the volatility smile generated by the model corresponds to a zero mean jump size, while the volatility skew corresponds to a negative mean jump size.     

Pricing errors and estimates of risk premia in factor models

In this paper, we consider the effect of the theoretical pricing error in the arbitrage pricing model on estimates of risk premia implied by the model. Under arbitrage pricing, the pricing error satisfies a strong bounding condition where for an infinite set of assets, the sum of squared pricing errors is bounded. We characterize the pricing error in terms of orders of probability and estimate an expected returns model which allows for pricing errors less than order one in probability. The principal finding of the paper is that misspecification of the pricing error and misspecification of the factor structure has no effect on the bias or mean squared error of the dominant risk premium. This implies that an exact form of arbitrage pricing can be used to estimate risk premia.     

Pricing and hedging European options with discrete-time coherent risk

The aim of the paper is to provide as explicit as possible expressions for upper/lower prices and for superhedging/subhedging strategies based on discrete-time coherent risk measures. This is done on three levels of generality. For a general infinite-dimensional model, we prove the fundamental theorem of asset pricing. For a general multidimensional model, we provide expressions for prices and hedges. For a wide class of models, in particular, including GARCH, we give more concrete formulas, a sufficient condition for the uniqueness of a hedging strategy, and a numerical algorithm.      

Pricing and risk of swing contracts in natural gas markets

Review of Derivatives Research - Motivated by the growing importance of swing contracts in natural gas markets, this article extends the literature on commodity price modelling as well as valuation...     

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

In this paper, we study inflation risk and the term structure of inflation risk premia in the United States' nominal interest rates through the Treasury Inflation Protection Securities (TIPS) with a multi-factor, modified quadratic term structure model with correlated real and inflation rates. We derive closed form solutions to the real and nominal term structures of interest rates that drastically facilitate the estimation of model parameters and improve the accuracy of the valuation of nominal rates and TIPS prices. In addition, we contribute to the literature by estimating the term structure of inflation risk premia implied from the TIPS market. The empirical evidence using data from the period of January 1998 through October 2007 indicates that the expected inflation rate, contrary to data derived from the consumer price indices, is very stable and the inflation risk premia exhibit a positive term structure.     

Pricing Weather Derivatives Using the Indifference Pricing Approach

Abstract

This paper adopts an incomplete market pricing model–the indifference pricing approach–to analyze valuation of weather derivatives and the viability of the weather derivatives market in a hedging context. It incorporates price risk, weather/quantity risk, and other risks in the financial market. In a mean-variance framework, the relationship between the actuarial price and the indifference price of weather derivatives is analyzed, and conditions are obtained concerning when the actuarial price does not provide an appropriate valuation for weather derivatives. Conditions for the viability of the weather derivatives market are examined. This paper also analyzes the effects of partial hedging, natural hedges, basis risk, quantity risk, and price risk on investors’ indifference prices by examining the distributional impacts of the stochastic variables involved.     

最大化你的定价权

根据最新的一项全球调研表明,只有35%的公司认为它们有足够的定价权来保证其产品能获得合适的定价;其余65%的公司认为它们没有将其产品定价到应该的高度,这意味着它们不得不接受利润缩水25%的现实。那些不具定价权的公司往往将责任推卸到外部因素,如激进的竞争对手和严苛的客户。但是,根据该调     

战略定价思与行

顾客价值对于保证公司的盈利无疑是非常重要的,需要引起公司高层管理者的重视。同时,销售、市场、运营和财务要通力合作。     

存款保险定价研究:期权定价法和预期损失定价法的进展

合理的存款保险定价可有效减少道德风险和逆向选择问题。本文梳理了国内外关于存款保险定价的两种主要方法——期权定价法和预期损失定价法及其最新发展情况。期权定价法的核心是将存款保险看作存款保险机构以银行资产为标的发行的一份看跌期权,之后学者从股利发放、监管宽容、系统性风险等多个角度进行拓展。预期损失定价法主要根据边际损失与边际保费收入相等来进行保费厘定,以探寻如何通过更科学的方法更精确地测量银行的预期损失。此外,本文讨论了存款保险定价方法对我国的启示。     

Pricing currency risk in the stock market: Evidence from Finland and Sweden 1970-2009

We investigate the role of currency risk on stock markets in two interlinked Nordic countries exhibiting a gradual move from fixed to floating exchange rates. We apply the Ding and Engle (2001) covariance stationary specification in a multivariate GARCH-M setup to test a conditional international asset pricing model. Using a sample period from 1970 to 2009, we find that the currency risk is priced in both stock markets, and that the price and the risk premium are lower after the floatation of the currencies, especially for Finland. We also find the cross-country exchange rate shock from Finland to affect the price of currency risk in Sweden, but not vice versa. Finally, we discuss some of the potential issues in applying multivariate GARCH-M specifications in tests of asset pricing models.     

Option Pricing Bounds and the Elasticity of the Pricing Kernel

In this paper we use power functions as pricing kernels to derive option-pricing bounds. We derive option pricing bounds given the bounds of the elasticity of the true pricing kernel. The bounds of the elasticity of the true pricing kernel are closely related to the bounds of the representative investor's coefficient of relative risk aversion. This methodology produces a tighter upper call option bound than traditional approaches. As a special case we show how to use the Black–Scholes formula to obtain option pricing bounds under the assumption of lognormality.     

Semi-analytical MBS Pricing

This paper presents a multi-factor valuation model for fixed-rate callable mortgage backed securities (MBS). The model yields semi-analytic solutions for the value of MBS in the sense that the MBS value is found by solving a system of ordinary differential equations. Instead of modelling the conditional prepayment rate (CPR), as is customary, the pool size is the primary modelling object. It is shown that the value of a single MBS payment due at time t _n can be found by computing two expectations of the pool size at time t _n–1 and t _n respectively. This is a general result independent of any interest rate model. However, if the pool size is specified in a way that makes the expectations solvable using transform methods, semi-analytic pricing formulas are achieved. The affine and quadratic pricing frameworks are combined to get flexible and sophisticated prepayment functions. We show that the model has no problem of generating negative convexity as the spot rate falls, and still be close to a similar non-callable bond when the spot rate rises.     

Pricing interest-rate-derivative securities

This article shows that the one-state-variable interest-ratemodels of Vasicek (1977) and Cox, Ingersoll, and Ross (1985b)can be extended so that they are consistent with both the currentterm structure of interest rates and either the current volatilitiesof all spot interest rates or the current volatilities of allforward interest rates. The extended Vasicek model is shownto be very tractable analytically. The article compares optionprices obtained using the extended Vasicek model with thoseobtained using a number of other models.     

Pricing growth-indexed bonds

Growth-indexed bonds have been suggested as a way of reducing the procyclicality of emerging-market countries’ fiscal policies and the likelihood of costly debt crises. Investor attitude surveys suggest that pricing difficulties are seen as a considerable obstacle. In an effort to reduce such concerns, this article presents a simple way of pricing growth-indexed bonds. As a pleasant by-product, the analysis tracks the quantitative implications of an increase in the share of growth-indexed bonds in total debt, measuring the ensuing decline in the probability of default and the reduction in the spreads at which standard bonds can be issued.     

金融资产定价与普通商品定价的比较研究

站在时间的维度上,我们可以更加清楚地了解一般商品价格理论和金融资产价格理论的区别和内在联系。一般商品的价格理论是构建在个体和厂商之上的一般均衡分析,从时间的维度看,它是一种面向历史的分析范式。金融资产的定价则是建立在无套利均衡思想上的资本化定价,从时间的维度看,它是一种面向未来的分析范式。     

Comparing Asset Pricing Models

A Bayesian asset pricing test is derived that is easily computed in closed form from the standard F‐statistic. Given a set of candidate traded factors, we develop a related test procedure that permits the computation of model probabilities for the collection of all possible pricing models that are based on subsets of the given factors. We find that the recent models of Hou, Xue, and Zhang (2015a, 2015b) and Fama and French (2015, 2016) are dominated by a variety of models that include a momentum factor, along with value and profitability factors that are updated monthly.