International Journal of Theoretical and Applied Finance

The drawdown of an asset is a risk measure defined in terms of the running maximum of the asset's spot price over some period [0, T]. The asset price is said to have drawn down by at least $K over this period if there exists a time at which the underlying is at least $K below its maximum-to-date. We introduce insurance against a large realization of maximum drawdown and a novel way to hedge the liability incurred by underwriting this insurance. Our proposed insurance pays a fixed amount should the maximum drawdown exceed some fixed threshold over a specified period. The need for this drawdown insurance would diminish should markets rise before they fall. Consequently, we propose a second kind of cheaper maximum drawdown insurance that pays a fixed amount contingent on the drawdown preceding a drawup. We propose double barrier options as hedges for both kinds of insurance against large maximum drawdowns. In fact for the second kind of insurance we show that the hedge is model-free. Since double barrier options do not trade liquidly in all markets, we examine the assumptions under which alternative hedges using either single barrier options or standard vanilla options can be used.

We present two statistical causes for the distortion of correlations on high-frequency financial data. We demonstrate that the asynchrony of trades as well as the decimalization of stock prices has a large impact on the decline of the correlation coefficients towards smaller return intervals (Epps effect). These distortions depend on the properties of the time series and are of purely statistical origin. We are able to present parameter-free compensation methods, which we validate in a model setup. Furthermore, the compensation methods are applied to high-frequency empirical data from the NYSE's TAQ database. A major fraction of the Epps effect can be compensated. The contribution of the presented causes is particularly high for stocks that are traded at low prices.

In this paper we explore the impact of various constant-proportions investment strategies (or Fixed-Mix Rules) in an economic evolutionary market. Dividends are generated according to a new Dividend Factor Model. Furthermore, dividends are estimated and calibrated from data using Principal Component Analysis. Moreover, we perform simulations to study the long-run outcome of an evolutionary competition with several well diversified constant-proportions strategies, among them some innovative strategies. We present and compare a variety of simulations with dividends being artificially generated according to our Dividend Model. Our simulation results are important for both theoretical and practical reasons. In theoretical terms we extend the existing numerical studies with the estimation and application of a more realistic model for the dividend process. In practical terms we suggest new constant-proportions strategies that could be superior for investors at least in the short run.

In this paper, we present a correction to Merton (1973)'s well-known classical case of pricing perpetual American put options by considering the same pricing problem under a stochastic volatility model with the assumption that the volatility is slowly varying. Two analytic formulae for the option price and the optimal exercise price of a perpetual American put option are derived, respectively. Upon comparing the results obtained from our analytic approximations with those calculated by a spectral collocation method, it is shown that our current approximation formulae provide fast and reasonably accurate numerical values of both option price and the optimal exercise price of a perpetual American put option, within the validity of the assumption we have made for the asymptotic expansion. We shall also show that the range of applicability of our formulae is remarkably wider than it was initially aimed for, after the original assumption on the order of the "volatility of volatility" being somewhat relaxed. Based on the newly-derived formulae, the quantitative effect of the stochastic volatility on the optimal exercise strategy of a perpetual American put option has also been discussed. A most noticeable and interesting result is that there is a special cut-off value for the spot variance, below which a perpetual American put option priced under the Heston model should be held longer than the case of the same option priced under the traditional Black-Scholes model, when the price of the underlying is falling.

We propose a parsimonious multi-asset Heston model and provide an easy-to-implement calibration algorithm. The model is customized to pricing multi-asset options in markets with liquidly traded single-asset options but no liquidly traded cross-asset options. In this situation, single-asset model parameters can be calibrated from option price data, however, cross-asset parameters cannot. We formulate a parsimonious model specification such that all single-asset models are Heston models, which are affine allowing for efficient calibration of the respective parameters. The single-asset models are correlated using cross-asset correlations only. Cross-asset correlations are observable, in contrast to correlations of latent variables such as volatilities, and serve as basis for calibration. A hybrid calibration approach for identifying the model parameters consistent with option price data and asset price data is outlined and illustrated by a case study. In banking practice the approach is referred to as correlation adjustment.

In this paper, the counterparty risk is considered in pricing a Credit Default Swap (abbr. CDS). We adopt an intensity-based reduced form model, in which the default intensity processes of the counterpart and the reference credit are modulated by the credit states of the firms. Two Markov chains are used to describe the credit state processes. We set up a model where the default correlation between the counterpart and the reference is described through the Markov chains. A semi-explicit formula for the pricing of CDS with counterparty risk is obtained. We analyze the impacts of default correlations and the state changes on the CDS price through some numerical experiments.

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes are provided and are shown to induce distinct implied volatility surfaces. The key features of the TC-FMR-SV framework are that (i) it is able to incorporate jumps into the price process of the underlying asset (ii) it allows for the leverage effect and (iii) it can accommodate multiple factors of volatility, which operate on different time-scales.