3,282 research outputs found
Local Variance Gamma and Explicit Calibration to Option Prices
In some options markets (e.g. commodities), options are listed with only a
single maturity for each underlying. In others, (e.g. equities, currencies),
options are listed with multiple maturities. In this paper, we provide an
algorithm for calibrating a pure jump Markov martingale model to match the
market prices of European options of multiple strikes and maturities. This
algorithm only requires solutions of several one-dimensional root-search
problems, as well as application of elementary functions. We show how to
construct a time-homogeneous process which meets a single smile, and a
piecewise time-homogeneous process which can meet multiple smiles
Stochastic Skew in Currency Options
We document the behavior of over-the-counter currency option prices across moneyness, maturity, and calendar time on two of the most actively traded currency pairs over the past eight years. We find that the risk-neutral distribution of currency returns is relatively symmetric on average. However, on any given date, the conditional currency return distribution can show strong asymmetry. This asymmetry varies greatly over time and often switch directions. We design and estimate a class of models that capture these unique features of the currency options prices and perform much better than traditional jump- diffusion stochastic volatility models.currency options, stochastic skew, time-changed Levy processes
The Finite Moment Log Stable Process and Option Pricing
We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.Volatility smirk; central limit theorem; Levy alpha-stable motion; selfsimilarity; option pricing.
What Type of Process Underlies Options? A Simple Robust Test
We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of atthemoney and outofthemoney options as the option maturity approaches zero. We show that these prices converge to zero at speeds which depend upon whether the sample path of the underlying asset price process is purely continuous, purely discontinuous, or a mixture of both. By applying the test to S&P 500 index options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump component. In particular, we find that while the presence of the jump component varies strongly over time, the presence of the continuous component is constantly felt. We investigate the implications of the evidence for parametric model specifications.Jumps; continuous martingale; option pricing; Levy density; double tails; local time.
Time-Changed Levy Processes and Option Pricing
As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that timechanged Levy processes be used to simultaneously address these three facets of the underlying asset return process. We show that our framework encompasses almost all of the models proposed in the option pricing literature. Despite the generality of our approach, we show that it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.random time change; Levy processes; characteristic functions; option pricing; exponential martingales; measure change
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
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