In the setting of ‘‘affine’ ’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks ’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

This paper develops an arbitrage-free time-series model of yields in continuous time that incorporates central bank policy. Policy-related events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linear-quadratic jump-diffusions as state variables, which allows for a wide variety of jump types but still leads to tractable solutions for bond prices. I estimate a version of this model with U.S. interest rates, the Federal Reserve’s target rate, and key macroeconomic aggregates. The estimated model improves bond pricing, especially at short maturities. The “snake-shape ” of the volatility curve is linked to monetary policy inertia. A new monetary policy shock series is obtained by assuming that the Fed reacts to information available right before the FOMC meeting. According to the estimated policy rule, the Fed is mainly reacting to information contained in the yield-curve. Surprises in analyst forecasts turn out to be merely temporary components of macro variables, so that the “hump-shaped” yield response to these surprises is not consistent with a Taylor-type policy rule.

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This paper studies the importance of the most commonly used factors in models of the term structure and contingent claims prices, as well as the importance of one seldom used factor. To this end, the paper develops a continuous-time, four-factor model of the term structure. The factors include the instantaneous interest rate, its volatility, its long-run mean, and a factor that is \independent " of, i.e., not a component of, the interest rate process. In addition, the model incorporates systematic jump risk in the interest rate process. Closed form solutions for bond prices are derived. Using the Fourier transform of a bond yield's transition density, we obtain continuous-time estimates for all parameters. Results indicate that jumps and volatility have a relatively minor impact on asset prices, with jumps being more important of the two at the long end of the yield curve and volatiliy more important in the middle. The interest rate, as expected, is the most important factor for the entire curve, particularly for the short end of the curve. The independent factor, seldom used in term structure models, is found to be the next most important factor on average, especially for the long end of the yield curve. The long-run mean is found to be important for the long end of the curve, as well, though not as important as the interest rate or

This paper implements a Multivariate Weighted Nonlinear Least Square estimator for a class of jump-diffusion interest rate processes (hereafter MWNLS-JD), which also admit closed- form solutions to bond prices under a no-arbitrage argument. The instantaneous interest rate is modeled as a mixture of a square-root diffusion process and a Poisson jump process. One can derive analytically the first four conditional moments, which form the basis of the MWNLS-JD estimator. A diagnostic conditional moment test can also be constructed from the fitted moment conditions. The market prices of diffusion and jump risks are calibrated by minimizing the pricing errors between a model-implied yield curve and a target yield curve. The time series estimation of the short-term interest rate suggests that the jump aug- mentation is highly significant and that the pure diffusion process is strongly rejected. The cross-sectional evidence indicates that the jump-diffusion yield curves are both more flexible in reducing pricing errors and are more consistent with the Martingale pricing principle.

We study a two-agent pure exchange equilibrium subject to both nondiversifiable di#usive andjumprisks. Agentscantradeinafinancialmarketconsistingofastockmarket,a money market, and an insurance market for jump risk. Heterogeneity is introduced through di#erent levels of relative risk aversion. In the framework of standard expected utility we find the surprising result that the more risk averse agent purchases insurance contracts against jump risk from the less risk averse agent. This equilibrium allocation is linked to the non-linear wealth sharing rule in such an economy, and preserves the wealth e#ects studied by Dumas (1989) in the case of pure di#usive risk. Since the benchmark economy with homogenous agents generates no excess uncertainty in the stock market, we study the e#ect on excess volatility and excess jump size solely due to di#erent levels of relative risk aversion. We observe up to 3% excess uncertainty for a reasonable specification of economic fundamentals.

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The Mexican mortgage market experienced significant turbulence in the 1990s allowing a newly created financial intermediary, the Sociedades Financieras de Objeto Limitado (SOFOLES) to gain entry into the low income mortgage market. The SOFOLES have instituted innovative loan origination and servicing policies and have spurred greater competition and specialization in the financial sector. Due to innovations and government rate subsidization, the SOFOLES ’ profits have been impressive. However, the question remains as to whether the SOFOLES can survive in a more competitive financial environment. The SOFOLES are pursuing securitization as the most desirable option for obtaining additional funding to expand their operations. The complexity of pricing SOFOLES mortgages has presented challenges to the securitization of their loans. Until recently the SOFOLES have received a government subsidy (FOVI): funding at a reduced interest rate. This subsidy is passed directly on to their mortgage holders in the form of below market interest rates on their loans. In an effort to expedite securitization, interest rate subsidies were

A regime switching model in continuous time is introduced where a variety of jumps are allowed in addition to the diffusive component. The characteristic function of the process is derived in closed form, and is subsequently employed to create the likelihood function. In addition, standard results of the option pricing literature can be employed in order to compute derivative prices. To this end, the relationship between the physical and the risk adjusted probability measure is explored. The generic relationship between Markov chains and [jump] diffusions is also investigated, and it is shown that virtually any stochastic volatility model model can be approximated arbitrarily well by a carefully chosen continuous time Markov chain. Therefore, the approach presented here can be utilized in order to estimate, filter and carry out option pricing for such continuous state-space models, without the need for simulation based approximations. An empirical example illustrates these contributions of the paper, estimating a stochastic volatility jump diffusion model.