Model-free price hedge ratios for homogeneous claims on tradable assets (original) (raw)
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This paper presents a comparison of alternative option pricing models based neither on jump-di usion nor stochastic volatility data generating processes. We assume either a smooth volatility function of some previously defined explanatory variables or a model in which discrete-based observations can be employed to estimate both path-dependence volatility and the negative correlation between volatility and underlying returns. Moreover, we also allow for liquidity frictions to recognize that underlying markets may not be fully integrated. The simplest models tend to present a superior out-of sample performance and a better hedging ability, although the model with liquidity costs seems to display better in-sample behavior. However, none of the models seems to be able to capture the rapidly changing distribution of the underlying index return or the net buying pressure characterizing option markets.
The Hypotheses Underlying the Pricing of Options
This paper gives a critical investigation on the hypotheses underlying the pricing of options. Even in recent articles on this subject many authors overlook the gaps in the original proof of the Black-Scholes option pricing formula, so the main goal of this note is to clarify firstly under which assumptions the formula remains true, and secondly repeat a correct proof of the mentioned formula. Probably this is justified by the fact that up to date even many text-books on this subject reproduce the wrong argumentation using erroneously the Black-Scholes hedge portfolio : obviously they missed the fact, that contrary to the claim of Black-Scholes, the change in value of the hedge portfolio in a short time interval is not riskless, an observation which was - as far as I know - firstly done by Y. Z. Bergman in his PH.D. Thesis, Berkeley 1982 and later on independently by W. Boge in Heidelberg in 1993.
investigaciones …, 2005
This paper presents a comparison of alternative option pricing models based neither on jump-diffusion nor stochastic volatility data generating processes. We assume either a smooth volatility function of some previously defined explanatory variables or a model in which discrete-based observations can be employed to estimate both path-dependence volatility and the negative correlation between volatility and underlying returns. Moreover, we also allow for liquidity frictions to recognize that underlying markets may not be fully integrated. The simplest models tend to present a superior out-of sample performance and a better hedging ability, although the model with liquidity costs seems to display better in-sample behavior. However, none of the models seems to be able to capture the rapidly changing distribution of the underlying index return or the net buying pressure characterizing option markets.
The Quarterly Review of Economics and Finance, 2004
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This paper investigates the pricing/hedging conundrum, i.e. the observation of a mismatch between derivatives models' pricing and hedging performances, that has so far been under-emphasized as the literature tends to focus on increasingly complicated option pricing models, without adequately addressing hedging performance. Hence, we analyze the ability of the Black-Scholes, Practitioner Black-Scholes, Heston-Nandi and Heston models to Deltahedge a set of call options on the S&P500 index and Apple stock. We extend earlier studies in that we consider the impact of asset dynamics, apply a stringent payoff replication strategy, look at the impact of moneyness at maturity and test for the robustness to the parameters' calibration frequency and Delta-Vega hedging. The study shows that adding risk factors to a model, such as stochastic volatility, should only be considered in light of the data dynamics. Even then, however, more complicated models generally fare poorly for hedging purposes. Hence, a better fit of a model to option prices is not a good indicator of its hedging performance, and so of its ability to describe the underlying dynamics. This can be understood for reasons of over-fitting. Those findings hint to a potentially appealing hedging-based calibration of models' parameters, rather than the standard pricing-based one.
Effectiveness of Classic Versions of Options Pricing Models in Recent Waves of Financial Upheavals
Asian Academy of Management Journal of Accounting and Finance, 2013
This paper attempts to determine the best alternative model of options pricing with the capacity to control both the level of skewness and kurtosis. It aims to replicate the effectiveness of classic stochastic and deterministic option pricing models and also establish a correlation between the underlying stock returns and their volatility. The paper follows a structural approach for analysing the Hull-White model (with two stochastic versions: non-related and correlated) with respect to the Black-Scholes model, which is a benchmark model. The focus is on fabricating such a model for predicting and protecting the market options price during uncertain financial upheavals. The suggested models have been tested in extreme conditions to determine effectiveness. Furthermore, the paper also examines the hedging effectiveness of hypothecated models.