Finite Maturity Research Articles

Pricing options on leveraged equity with default risk and exponentially increasing, finite maturity debt

We extend a modular pricing framework proposed by Ericsson and Reneby (Appl. Math. Finance 5 (1998) 143; Stock options as barrier contingent claims, Working Paper, Stockholm School of Economics; The valuation of corporate liabilities: theory and tests, Working Paper, Stockholm School of Economics) to derive a valuation formula for calls on leveraged equity, similar to Toft and Prucyk (J. Finance LII (1997) 1151). In contrast to their derivation via partial differential equations, we choose a more elegant probabilistic approach using change of numeraire techniques. Considerably extending previous firm-value-based option pricing models, our framework features exponentially increasing, finite maturity coupon debt, along with taxes and deviations from absolute priority. It enables us to study effects of debt maturity and debt growth on prices of equity options. Numerical results provide new insights into possible causes for pricing biases of the Black–Scholes formula.

Pricing Options on Leveraged Equity with Default Risk and Exponentially Increasing, Finite Maturity Debt

We extend a modular pricing framework proposed by Ericsson and Reneby (1998, 2000, 2001) to derive a valuation formula for calls on leveraged equity, similar to Toft and Prucyk (1997). In contrast to their derivation via partial differential equations, we choose a more elegant probabilistic approach using change of numeraire techniques. Considerably extending previous firm value based option pricing models, our framework features exponentially increasing, finite maturity coupon debt, along with taxes and deviations from absolute priority. It enables us to study effects of debt maturity and debt growth on prices of equity options. Numerical results provide new insights into possible causes for pricing biases of the Black-Scholes formula.

Liquidity and Credit Risk

We develop a structural bond valuation model to simultaneously capture liquidity and credit risk. Our model implies that renegotiation in financial distress is influenced by the illiquidity of the market for distressed debt. As default becomes more likely, the components of bond yield spreads attributable to illiquidity increase. When we consider finite maturity debt, we find decreasing and convex term structures of liquidity spreads. Using bond price data spanning 15 years, we find evidence of a positive correlation between the illiquidity and default components of yield spreads as well as support for downward sloping term structures of liquidity spreads.

Rational Equilibrium Asset-Pricing Bubbles in Continuous Trading Models

We study rational equilibrium asset-pricing bubbles in an economic environment in which agents are allowed to trade continuously, including as special cases some models from financial economics. For positive net supply assets, we present new necessary and sufficient conditions for the absence of bubbles in complete and incomplete markets equilibria with several types of borrowing constraints. For zero net supply assets, including financial derivatives with finite maturities, we show that bubbles can generally exist and have properties different from their discrete-time, infinite-horizon counterparts. We introduce a probabilistic approach to studying bubbles, generalizing analogs of existing results in the discrete-time bubbles literature. Journal of Economic Literature Classification Numbers: D50, G12, G13.

Formules quasi-explicites pour les options américaines dans un modèle de diffusion avec sauts

This paper proposes two quasi-explicit formulas to calculate the American option prices with finite and infinite maturity respectively, in Merton's jump-diffusion model (1976).

Interest Rate Innovations and the Volatility of Long-Term Bond Yields

This paper develops and tests restrictions on the variance of innovations in long-term bond yields implied by the expectations model of the term structure. The authors adapt Kenneth D. West's (1988) stock-price volatility tests to the case of long but finite maturity bonds. Their approximate equality restriction does not require short-term rates to be stationary and, hence, provides a unified framework for volatility testing. When short rates are modeled as stationary, long-rate innovations appear excessively volatile. When short rates are modeled as difference stationary, long-rate innovations appear excessively smooth. Copyright 1994 by Ohio State University Press.

Benchmarks for stochastic models

A new diversity of financial instruments available to investors has blurred the distinction between fixed-income and other types of securities. In general, all securities represent state-contingent claims either to cash flows or to the market value of the assets legally owned by the securityholder, or both. Viewed in the context of the issuing entity's balance sheet, financial instruments are liabilities cast as either debt or equity. Broadly speaking, fixed-income securities are debt securities. Typically, fixed-income securities have the following characteristics: 1) a finite life or maturity; 2) a stated payment of cash flows, or a stated set of rules for determining cash flows (hence, the term fixed income); and 3) in the event of failure to comply with the stated cash flow rules, legal remedies and some degree of seniority of rights over pure equityholders and, perhaps, over other fixed-income securityholders. In two decades the fixed-income market has grown in magnitude and complexity. Fixed-income investors can choose from a wide array of fixed, floating, inverse floating, interest-only (IO), principal-only (PO), callable, putable, prepay-protected, prepayadvantaged, pay-in-kind or convertible debt securities, to name a few. They can swap fixed for floating interest payments, buy or sell options on securities, options on options, and options on swaps. They can buy bonds that redeem principal based on the price of oil, the price of gold, 0r.a currency exchange can buy debt in default. Innovative rate. Investors techniques to restructure bond cash flows also enable investors to purchase derivative securities that bear little or no resemblance to the underlying debt, except through complete recombination.