Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

Asset pricing theory for two price economies

We show that nonlinearly discounted nonlinear martingales are related to no arbitrage in two price economies as linearly discounted martingales were related to no arbitrage in economies satisfying the law of one price. Furthermore, assuming risk acceptability requires a positive physical expectation, we demonstrate that expected rates of return on ask prices should be dominated by expected rates of return on bid prices. A preliminary investigation conducted here, supports this hypothesis. In general we observe that asset pricing theory in two price economies leads to asset pricing inequalities. A model incorporating both nonlinear discounting and nonlinear martingales is developed for the valuation of contingent claims in two price economies. Examples illustrate the interactions present between the severity of measure changes and their associated discount rates. As a consequence arbitrage free two price economies can involve unique discount curves and measure changes that are however specific to both the product being priced and the trade direction. Furthermore the developed valuation operators call into question the current practice of Debt Valuation Adjustments.     

An arbitrage model of the term structure of interest rates

A formula for the price of default-free discount bonds of all maturities is found using a Black- Scholes type of arbitrage model which is based on the assumption that a portfolio of three default-free discount bonds of distinct maturities can be managed to be a perfect substitute for any other default-free discount bond. The formula relates the price of bonds to the real rate of interest, the anticipated rate of inflation and the equilibrium prices of interest rate and inflation risks. Bond prices are shown to be the expected value of the sure nominal proceeds of the bond discounted to the present at a random discount rate. It is shown that the unbiased expectations hypothesis is in general inconsistent with this model.     

A continuous time approach to the pricing of bonds

This paper develops an arbitrage model of the term structure of interest rates based on the assumptions that the whole term structure at any point in time may be expressed as a function of the yields on the longest and shortest maturity default free instruments and that these two yields follow a Gauss-Wiener process. Arbitrage arguments are used to derive a partial differential equation which must be satisfied by the values of all default free bonds. The joint stochastic process for the two yields is estimated using Canadian data and the model is used to price a sample of Government of Canada bonds.     

Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model

We develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. We derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed-form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model.     

人民币对美元利率平价分析

引入外汇价格和存贷利率因素,把利率平价模型变得更贴近经济运行的实际情况,由此计算出在抛补利率平价模型下隐含的美元利率。运用此理论对中国实证发现,隐含美元利率和现实美元利率之间存在很大利差。各微观金融交易主体几乎没有利率自主权以及资本项目不可自由兑换是存在套利空间的主要原因。要消除美元套利空间,首先要掌握人民币外汇远期定价权;其次,要逐步开放资本项目,实现人民币的自由浮动和国际化;最后要完善汇率体制改革和加强国际间的协调。     

Noise Trading, Costly Arbitrage, and Asset Prices: Evidence from Closed-end Funds

If arbitrage is costly and noise traders are active, asset prices may deviate from fundamental values for long periods of time. We use a sample of 158 closed-end funds to show that noise-trader sentiment, as proxied by retail-investor flows, leads to fluctuations in the discount. Nevertheless, we reject the hypothesis that noise-trader risk is the cause of the long-run discount. Instead we find that funds which are more difficult to arbitrage have larger discounts, due to: (1) the censoring of the discount by the arbitrage bounds, and (2) the freedom of managers to increase charges when arbitrage is costly.     

Call Options, Points, and Dominance Restrictions on Debt Contracts

We analyze the impact of a contract's length, callability, amortization, and original discount by arbitrage methods. Among instruments that are callable without penalty, longer instruments command a higher interest rate because the borrower possesses the option of repaying relatively more slowly. However, the rate on longer self-amortizing loans cannot be substantially larger than for shorter ones because the payments decrease with contract length. Bounds on the trade-off between points and rate for callable debt are characterized using the trade-off for noncallable debt and the property that the value of the prepayment option increases with the loan's interest rate.     

Exact solutions for bond and option prices with systematic jump risk

A variety of realistic economic considerations make jump-diffusion models of interest rate dynamics an appealing modeling choice to price interest-rate contingent claims. However, exact closed-form solutions for bond prices when interest rates follow a mixed jump-diffusion process have proved very hard to derive. This paper puts forward two new models of interest-rate dynamics that combine infrequent, discrete changes in the interest-rate level, modeled as a jump process, with short-lived, mean reverting shocks, modeled as a diffusion process. The two models differ in the way jumps affect the central tendency of interest rates; in one case shocks are temporary, in the other shocks are permanent. We derive exact closed-form solutions for the price of a discount bond and computationally tractable schemes to price bond options.     

The valuation of catastrophe bonds with exposure to currency exchange risk

In this paper, we present a new model that takes an arbitrage approach to the valuation of catastrophic risk bonds (CAT bonds). The model considers the sponsor's exposure to currency exchange risk and the risk of catastrophic events. We use a jump-diffusion process for catastrophic events, a three-dimensional stochastic process for the exchange rate and domestic and foreign interest rates, and a hedging cost for the currency risk to derive a semi-closed-form formula for the CAT bond price. We also extend to three factors Joshi and Leung's (2007) Monte Carlo simulation approach to obtain numerical results showing the following: in addition to catastrophic risk, the CAT bond price is affected mainly by the volatility of the exchange rate and its correlations with domestic and foreign interest rates. The first two factors have a negative impact while the third has a positive impact.     

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions

Equity release products are sorely needed in an aging population with high levels of home ownership. There has been a growing literature analyzing risk components and capital adequacy of reverse mortgages in recent years. However, little research has been done on the risk analysis of other equity release products, such as home reversion contracts. This is partly due to the dominance of reverse mortgage products in equity release markets worldwide. In this article we compare cash flows and risk profiles from the provider's perspective for reverse mortgage and home reversion contracts. An at-home/in long-term care split termination model is employed to calculate termination rates, and a vector autoregressive (VAR) model is used to depict the joint dynamics of economic variables including interest rates, house prices, and rental yields. We derive stochastic discount factors from the no arbitrage condition and price the no negative equity guarantee in reverse mortgages and the lease for life agreement in the home reversion plan accordingly. We compare expected payoffs and assess riskiness of these two equity release products via commonly used risk measures: Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).     

International tax arbitrage,financial parity conditions and preferential capital gains taxation

Using a finite-horizon general equilibrium model with uncertainty and money, we characterize situations where tax arbitrage opportunities may arise for international portfolio investors in an economy with heterogeneous capital income taxation when interest income and capital gains/losses are taxed differentially for some agents. We derive tax-modified uncovered interest parity conditions, Fisher conditions and forward prices similar to the no-tax ones, but augmented by tax-induced ‘risk-premium’ terms; covered interest parity and Fisher conditions remain unaffected by the introduction of capital income taxes as we bound tax-based arbitrage without restricting arbitrage per se.     

票据市场利率体系及其与银行间货币市场整体利率的关系

我国的商业汇票利率体系主要由承兑费率、贴现利率、转贴现利率和再贴现利率构成。其中作为银行间市场业务的票据转贴现，其利率已实现市场化。在监管部门加大力度规范会计科目核算、严查逃避信贷规模的票据业务后，买断性日趋明显，其利率更多受到信贷规模影响，与其它银行间货币市场利率产生了一定背离；回购式转贴现业务则逐步脱离规模互转方式，近期呈现了较强的资金业务特性，利率水平逐步接轨其它银行间货币市场利率。     

The dividend-price ratio and expectations of future dividends and discount factors

A dividend-ratio model is introduced here that makes the logof the dividend-price ratio on a stock linear in optimally forecastfuture one-period real discount rates and future one-periodgrowth rates of real dividends. If ex post discount rates areobservable, this model can be tested by using vector autoregressivemethods. Four versions of the linearized model, differing inthe measure of discount rates, are tested for U.S. time series1871-1986 and 1926-1986: a version that imposes constant realdiscount rates, and versions that measure discount rates fromreal interest rate data, aggregate real consumption data, andreturn variance data. The results yield a metric to judge therelative importance of real dividend growth, measured real discountrates, and unexplained factors in determining the dividend-priceratio.     

Term Structure Movements and Pricing Interest Rate Contingent Claims

This paper derives an arbitrage-free interest rate movements model (AR model). This model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free. We then show that the AR model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates. This paper also studies the behavior and the economics of the model. Our approach can be used to price a broad range of interest rate contingent claims, including bond options and callable bonds.     

Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.     

Consistent valuation of project finance and LBOs using the flows‐to‐equity method

The flows‐to‐equity method is used to value transactions where debt amortizes according to a fixed schedule, requiring a formula that links the changing leverage with a time‐varying equity discount rate. We show that extant formulas yield incorrect valuations because they are inconsistent with the basic assumptions of this method. The error from using the wrong formula can be large, especially at currently low interest rates. We derive a formula that captures the effects of a fixed debt plan, potentially expensive debt, and costs of financial distress. We resolve an important issue about what to use as the cost of debt.     

Can interest rate factors explain exchange rate fluctuations?

The level, slope, and curvature of the yield curve reflect time variation in investors’ risk premia and are known predictors of excess bond returns and economic activity. In this paper, I develop a term structure model under complete markets and no arbitrage to relate these interest rate factors to exchange rate fluctuations. The Gaussian properties of the stochastic discount factors imply non-linearities in exchange rate risk premia that are shown to account for up to half of the in-sample variation in one-year currency returns for different country pairs during the 1980s–2015 period. I find that interest rate factors help explain exchange rate fluctuations in and out of sample, particularly at longer horizons, and yield profitable currency portfolios relative to standard carry trade strategies.     

A Note on Option Pricing for the Constant Elasticity of Variance Model

We study the arbitrage free optionpricing problem for the constant elasticity of variance (CEV) model. To treatthestochastic aspect of the CEV model, we direct attention to the relationship between the CEV modeland squared Bessel processes. Then we show the existence of a unique equivalentmartingale measure and derive the Cox's arbitrage free option pricing formulathrough the properties of squared Bessel processes. Finally we show that the CEVmodel admits arbitrage opportunities when it is conditioned to be strictlypositive.     

Asian option pricing with orthogonal polynomials

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black–Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. We provide sufficient conditions to guarantee convergence of the series. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however we show numerically that the bias can safely be ignored in practice.