Pricing interest rate contingent claims

This thesis extends the previous work on interest rate contingent claims in several ways. First, futures pricing models and futures options pricing models are derived. These models are under the settings of both single state variable and two state variables. The derivations make use of regular techniques in solving partial differential equations and the risk-neutral pricing methodology.Second, the forward price valuation process helps to find the futures price under discrete marking to market. The derivation makes use of a simple concept: finding a futures price under discrete marking to market is finding a sequence of forward prices. This simple technique can also help us to decide whether or not closed form solutions exist.Last, numerical results on options confirm that interest rate futures options can not be priced by either Black's model for commodity futures options or Jamshidian's model for bond options. Numerical results on forward prices and futures prices, on the other hand, tells an opposite story. It is found that the difference between the two prices is always less than 2%. This finding reduces the significance of the discrete marking to market model for futures contracts. A simple test on the one factor futures pricing model shows that the model is not supported by the data.U of I OnlyETDs are only available to UIUC Users without author permissio

Carry Cost Rate Regimes and Futures Hedge Ratio Variation

This paper tests whether the traditional futures hedge ratio (hT) and the carry cost rate futures hedge ratio (hc) vary in accordance with the Sercu and Wu (2000) and Leistikow et al. (2019) “hc” theory. It does so, both within and across high and low spot asset carry cost rate (c) regimes. The high and low c regimes are specified by asset across time and across currency denominations. The findings are consistent with the theory. Within and across c regimes, hT is inefficient and hc is biased. Across c regimes, hc’s Bias Adjustment Multiplier (BAM) does not vary significantly. Even though hc’s bias-adjusted variant’s BAM is restricted to old data that is from a different c regime, the hedging performance of hc and its bias-adjusted variant (=hc × BAM), are superior to that for hT. Variation in c may account for the hT variation noted in the literature and variation in c should be incorporated into ex ante hedge ratios

A universal lattice

When valuing derivative contracts with lattice methods, one often needs different lattice structures for different stochastic processes, different parameter values, or even different time intervals to obtain positive probabilities. In view of this stability problem, in this paper, we derive a trinomial lattice structure that can be universally applied to any diffusion process for any set of parameter values at any given time interval. It is particularly useful to the processes that cannot be transformed into constant diffusion. This lattice structure is unique in that it does not require branches to recombine but allows the lattice to freely evolve within the prespecified state space. This is in spirit similar to the implicit finite difference method. We demonstrate that this lattice model is easy to follow and program. The universal lattice is applied to time and state dependent processes that have recently become popular in pricing interest rate derivatives. Numerical examples are provided to demonstrate the mechanism of the model. Copyright Kluwer Academic Publishers 1999