• Selected
• Entire List

Abstract:
In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model with a constant recovery rate outperforms the market practice of directly comparing bonds' credit spreads to default swap premiums. We find that the model works well for investment grade credit default swaps, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is insensitive to the value of the assumed recovery rate.

credit default swaps, credit derivatives, credit risk, default risk, risk-neutral valuation, default-free interest rates

Abstract:
We consider eight different proxies (issued amount, coupon, listed, age, missing prices, yield volatility, number of contributors and yield dispersion) to measure corporate bond liquidity and use a five-variable model to control for interest rate risk, credit risk, maturity, rating and currency differences between bonds. The null hypothesis that liquidity risk is not priced in our data set of euro corporate bonds is rejected for seven out of eight liquidity proxies. We find significant liquidity premia, ranging from 9 to 24 basis points. A comparison test between liquidity proxies shows limited differences between the proxies.

liquidity, premiums, spreads, credit, corporate bonds, yields, fama-french model

Abstract:
In this paper we develop a new method to value American stock options with stochastic interest rates. We construct a binomial tree for the stock price divided by the price of the zero coupon bond that matures at the maturity date of the option. In fact, we construct a tree for the so-called forward risk adjusted measure. In each node of the tree the quotient of the stock price and bond price is constant and there are combinations of stock and bond prices for which immediate exercise is optimal and other combinations for which this is not the case. We derive for each node in the tree an analytic expression for the expected immediate exercise premium conditional on this quotient of stock and bond prices. This immediate exercise premium is added to the value that is derived from the familiar backward procedure. Both European and American option prices depend on the correlation between the interest rate process and the stock price process. It is interesting to see that with increasing correlation between the interest rate process and the stock price process, and hence a decreasing correlation between bond and stock prices, the values of European options increase, while the values of the early exercise premium decrease. For American options this might result in a non-monotonic relation between the correlation coefficient and the option price. Furthermore, there is evidence that the early exercise premium due to stochastic interest rates is much larger than established before by other researchers. Finally, we also consider the influence of the shape of the initial term structure.

Abstract:
In this paper we develop a new method to value American stock options with stochastic interest rates. We construct a binomial tree for the stock price divided by the price of the zero coupon bond that matures at the maturity date of the option. In fact, we construct a tree for the so-called forward risk adjusted measure. In each node of the tree the quotient of the stock price and bond price is constant and there are combinations of stock and bond prices for which immediate exercise is optimal and other combinations for which this is not the case. We derive for each node in the tree an analytic expression for the expected immediate exercise premium conditional on this quotient of stock and bond prices. This immediate exercise premium is added to the value that is derived from the familiar backward procedure. Both European and American option prices depend on the correlation between the interest rate process and the stock price process. It is interesting to see that with increasing correlation between the interest rate process and the stock price process, and hence a decreasing correlation between bond and stock prices, the values of European options increase, while the values of the early exercise premium decrease. For American options this might result in a non-monotonic relation between the correlation coefficient and the option price. Furthermore, there is evidence that the early exercise premium due to stochastic interest rates is much larger than established before by other researchers. Finally, we also consider the influence of the shape of the initial term structure.

Abstract:
We value rating-triggered step-up bonds with three methods: (i) the Jarrow, Lando and Turnbull [1997, JLT] framework, (ii) a similar framework using historical probabilities and (iii) as plain vanilla bonds. We find that the market seems to value single step-up bonds according to the JLT model, while it values multiple step-up bonds as plain vanilla bonds. Further, step-up feature market premiums are more volatile than JLT and historical premiums, and the JLT model approximates market premiums always better than the historical method. Finally, most step-up bonds offer a cushion against rating migrations via dampened price movements.

step-up bonds, rating-triggered, credit risk, reduced form models, Jarrow Lando Turnbull

Abstract:
Abstract: In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model with a constant recovery rate outperforms the market practice of directly comparing bonds' credit spreads to default swap premiums. We find that the model works well for investment grade credit default swaps, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is insensitive to the value of the assumed recovery rate. Keywords: credit default swaps, credit derivatives, credit risk, default risk, default-free interest rates

credit default swaps, credit derivatives, credit risk, default risk, default-free interest rates, market prices, empirical models

Abstract:
In this paper we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility. Extensive research has clearly demonstrated that the volatility of most stocks is not constant over time. As small changes of the volatility can have a major impact on the value of contingent claims, hedging strategies should try to eliminate this volatility risk. We propose a stochastic optimization model for hedging contingent claims that takes into account the effects of stochastic volatility, transaction costs and trading restrictions. Simulation results show that our approach could improve performance considerably compared to traditional hedging strategies.

Option hedging, Stochastic Volatility, Stochastic Programming, Computational Finance

Abstract:
In this paper we study the impact of earnings announcements on trading volume, open interest and spreads in the stock option market. We find that option volume is higher around announcement days, even if we correct for stock volume and the expected future volatility of stock returns. Results in the pre-event period are different for good and bad news samples, indicating that option traders have access to (possibly short lived) private information. During the days before the announcements open interest tends to increase. After the earnings news dissemination traders seem to lose interest in the contracts and cancel part of their option positions thereby reducing open interest to normal levels. Analysis of quoted spreads provide no evidence of dealers' anticipation of higher information asymmetry in the pre- or post announcement period. However, results for effective spreads indicate that the transaction costs are higher on the announcement day itself and on the day immediately following the earnings dissemination. Both quoted and effective spreads are shown to respond to changes in trading volume and expected return variability.

Earnings Announcements, Volatility, Volume, Spreads, Open Interest

Abstract:
We study the implied volatility behavior of European Options Exchange call option prices around scheduled news announcement days of the underlying stock. Implied volatilities significantly increase during the pre-event period and reach a maximum at the eve of the news announcement. After the news release, the implied volatility drops sharply and is at its minimum four days after the news release. From that point on it gradually moves back to its long run level. These results also hold if implied volatilities are corrected for market-wide changes in volatility by subtracting the implied volatility of the EOE-index or the average implied volatility of a group of control stocks. The volatility of the underlying stocks does not change during the pre- and post-event period. Only at the event date itself movements in the price of the underlying stock are significantly larger than expected, given mean and standard deviation of the stock returns in the control period. Hence, volatility of the underlying assets seems to be higher only on event days. We give an option pricing model based on this one-time jump in volatility. The model implicates a pattern of changes in implied volatilities that roughly agrees with the above described pattern. We test two trading strategies that may profit from the movements in implied volatilities and find that the results are statistically insignificant.

Abstract:
Index-futures arbitrageurs enter into the market only if the deviation from the arbitrage relation is large enough to compensate for transaction costs and associated interest-rate and dividend risks. Using a threshold autoregression model for the mispricing error, we estimate the band around the theoretical futures prices within which arbitrage is not profitable for most arbitrageurs. Combining these thresholds with an error correction model, we can make a distinction between the effects of arbitrageurs and infrequent trading on index and futures returns. The impact of the mispricing error on the returns is increasing with the magnitude of the mispricing error, and the effect of futures returns on index returns is significantly larger when the basis is negative.

Abstract:
Some of the most recent empirical studies on interest rate derivatives have found humped shapes in the volatility structure of interest rates. Accordingly, Mercurio and Moraleda (1996) have modeled interest rate dynamics in a way that allows for such a shape in the volatility and is analytically very tractable. Unfortunately, their model cannot be used for pricing American style claims with a recombining lattice. This paper proposes, similarly to Mercurio and Moraleda (1996), a humped volatility of interest rates model that not only gives explicit formulas for European options on discount bonds but also allows for pricing American options in a recombining lattice. In fact, it can be embedded in either the Hull and White (1993, 1994, 1995) tree or the Li, Ritchken and Sankarasubramanian (1995) lattice. The paper shows, furthermore, that if a deterministic volatility model can be embedded in either of these algorithms then so does it in the other one. It is also proved that it is not possible to find a volatility of the class proposed by Mercurio and Moraleda (1996) such that American style claims can be priced using a Markovian process for the spot rate.

Abstract:
There exist a number of approximation methods for the price of average rate options, when the underlying asset is a currency or equity. Realistic pricing models for average interest rate caps based on interbank offered rates have not yet been published. In this paper, we propose to adapt the methods of Levy (1992), Vorst (1992) and Rogers and Shi (1995) for average rate options to price average interest rate caps and compare their computational efficiencies. All three methods are very fast, compared to the Monte Carlo simulation. Two of them are fast enough for on-the-fly calculations. The underlying interest rate model we use is consistent with the observed term structure of interest rate. Hence, the models developed here are suitable for practical implementation.

Abstract:
It is common to find index funds being marketed with a protective floor. It gives investors the upside potential of the equity market, while protecting them from possible losses. In this paper, we describe a new type of protective floor, in which the floor level is not set at inception of the contract. Instead, during the contract life, the holder can give notice --- he shouts --- to set the floor at the prevailing index level. It is shown in the paper, that the optimal shout policy does not depend on the index level, but only on time-to-maturity. The concept is generalized further to multiple-shout floors. If the index hits a higher level after the first shout, the holder is allowed to shout again to reset the floor at the then prevailing (higher) index level. An efficient numerical model is proposed to price the multiple-shout floors.

Abstract:
This article develops a new trinomial tree model for barrier options. It is well-known that for barrier options, the positions of nodes in the tree with respect to the barrier value are critical. We use a time-dependent shift to position the tree optimally with respect to the barrier. The model is very flexible and can be used to price options with time-varying barrier structures. It can be used to price knock-in and knock-out options based on either one or two underlying assets, including those with time-varying barriers - single or double. Traditional lattice models all have difficulties when the underlying asset price is very close to the barrier. This model does not suffer from that limitation. Also, in many applications, the barrier condition is based on the daily or weekly fixings. A simple solution for the discrete-time barrier observation is advanced, which enables us to uncover the price differences among barrier options with different observation frequencies.