Probability weighting functions obtained from Hong Kong index option market

In this paper we estimate the pricing kernel from the Hong Kong index option market and obtain the empirical probability weighting functions based on the rank-dependent expected utility. The empirical pricing kernel is estimated semi-parametrically as the ratio of the risk-neutral and objective densities. We employ a two-step estimation procedure to estimate the objective and risk-neutral densities under a consistent parametric framework of the non-affine generalised autoregressive conditional heteroskedasticity (G.A.R.C.H.) diffusion model. In the first step, we develop a continuous particle filters-based maximum likelihood estimation method to estimate the objective parameters of the G.A.R.C.H. diffusion model using the Hang Seng Index (H.S.I.) returns. In the second step of our estimation, we depart from the usual pure calibration approach and use the H.S.I. option prices to estimate the risk-neutral parameters of the G.A.R.C.H. diffusion model by constraining certain parameters to be consistent with the time-series behaviour of H.S.I. returns. Based on the estimated objective and risk-neutral parameters, the objective and risk-neutral densities are obtained by inverting the corresponding characteristic functions. Empirical results indicate that the empirical pricing kernel estimated from the Hong Kong index option market is non-monotonic and the estimated probability weighting functions are S-shaped, which implies that investors underweight small probability events and overweight large one

An empirical comparison of the performance of alternative option pricing models

Published as an article in: Investigaciones Economicas, 2005, vol. 29, issue 3, pages 483-523.option pricing, conditional volatility, SNN Nonparametric estimator

Risk preference discrepancy : a prospect relativity account of the discrepancy between risk preferences in laboratory gambles and real world investments

In this article, we presented evidence that people are more risk averse when investing in financial products in the real world than when they make risky choices between gambles in laboratory experiments. In order to provide an account for this discrepancy, we conducted experiments, which showed that the range of offered investment funds that vary in their riskreward characteristics had a significant effect on the distribution of hypothetical funds to those products. We also showed that people are able to use the context provided by the choice set in order the make relative riskiness judgments for investment products. This context dependent relativistic nature of risk preferences is proposed as a plausible explanation of the risk preference discrepancy between laboratory experiments and real-world investments. We also discuss other possible theoretical interpretations of the discrepancy

An analysis of spending behaviour under liquidity constraints with an application to financial hedging

Imperial Users onl

Using financial futures in trading and risk management

The authors explain the features of an array of futures contracts and their basic pricing relationships and describe a few applications to show how investors and risk managers can use these contracts. Futures - and derivatives generally - allow economic agents to fine-tune the structure of their assets and liabilities to suit their risk preferences and market expectations. Futures are not a financing or investment vehicle per se, but a tool for transferring price risks associated with fluctuations in asset values. Some may use them to spread risk, others to take on risk. Financial futures (along with options) are best viewed as building blocks. Futures have facilitated the modern trend of separating conventional financial products into their basic components. They allow not only the reduction of transformation of investment risk but also the understanding and measurement of risk. The market for derivatives has grown enormously over the past decade. The value of exchange-traded eurodollar derivatives (futures and options) is equal to roughly 13 times the value of the underlying market. The volume of trading in financial futures now dwarfs the volume in traditional agricultural contracts. As emerging markets develop, given their inherently risky nature, expect financial futures to play a prominent role in risk management.Payment Systems&Infrastructure,Economic Theory&Research,International Terrorism&Counterterrorism,Banks&Banking Reform,Securities Markets Policy&Regulation,Commodities,Banks&Banking Reform,International Terrorism&Counterterrorism,Non Bank Financial Institutions,Economic Theory&Research

Static Hedging of Standard Options

We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this portfolio of shorter-term options, the portfolio weights do not vary with the underlying asset price or calendar time. We then implement this static relation using a finite set of shorter-term options and use Monte Carlo simulation to determine the hedging error thereby introduced. We compare this hedging error to that of a delta hedging strategy based on daily rebalancing in the underlying futures. The simulation results indicate that the two types of hedging strategies exhibit comparable performance in the classic Black-Scholes environment, but that our static hedge strongly outperforms delta hedging when the underlying asset price is governed by Merton (1976)'s jump-diffusion model. The conclusions are unchanged when we switch to ad hoc static and dynamic hedging practices necessitated by a lack of knowledge of the driving process. Further simulations indicate that the inferior performance of the delta hedge in the presence of jumps cannot be improved upon by increasing the rebalancing frequency. In contrast, the superior performance of the static hedging strategy can be further enhanced by using more strikes or by optimizing on the common maturity in the hedge portfolio. We also compare the hedging effectiveness of the two types of strategies using more than six years of data on S&P 500 index options. We find that in all cases considered, a static hedge using just five call options outperforms daily delta hedging with the underlying futures. The consistency of this result with our jump model simulations lends empirical support for the existence of jumps of random size in the movement of the S&P 500 index. We also find that the performance of our static hedge deteriorates moderately as we increase the gap between the maturity of the target call option and the common maturity of the call options in the hedge portfolio. We interpret this result as evidence of additional random factors such as stochastic volatility.Static hedging, jumps, option pricing, Monte Carlo, S&P 500 index options, stochastic volatility

Variance Risk Premia

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.Stochastic volatility, variance risk premia, variance swap, volatility swap, option pricing, expectation hypothesis

Single Stock Call Options as Lottery Tickets:Overpricing and Investor Sentiment

The authors investigate whether the overpricing of out-of-the money single stock calls can be explained by Tversky and Kahneman's [1992] cumulative prospect theory (CPT). They hypothesize that these options are expensive because investors overweight small probability events and overpay for positively skewed securities (i.e., lottery tickets). The authors find that overweighting of small probabilities embedded in the CPT explains the richness of out-of-the money single stock calls better than other utility functions. Nevertheless, overweighting of small probabilities events is less pronounced than suggested by the CPT, is strongly time varying, and most frequent in options of short maturity. The authors find that fluctuations in overweighting of small probabilities are largely explained by the sentiment factor