4,400 research outputs found
Option bounds for multinomial stock returns in Jump-Diffusion processes - a Monte Carlo simulation for a multi-jump process
This paper addresses the problem of option bounds computation under the assumption that the price of the underlying asset follows a jump-diffusion Merton process as formulated in Perrakis (1993) extending the number of the jumps from one jump up and one jump down with fixed sizes to a finite number of jumps with sizes drawn from the lognormal distribution. The objective of this paper is to create a Monte Carlo simulation for the estimation of the bounds with various numbers of jumps and periods to maturity.Monte Carlo simulation, Jump-Diffusion processes, multi-jump process
Modelling FX smile : from stochastic volatility to skewness
Imperial Users onl
Parametric and Nonparametric Volatility Measurement
Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the ex-post sample-path return variability over a fixed time interval, (ii) the ex-ante expected volatility over a fixed time interval, and (iii) the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discrete-time ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete- and continuous-time stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recently-popularized realized volatility measures for (non-trivial) fixed-length time intervals.
Parametric and Nonparametric Volatility Measurement
Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuous-time, frictionless, no-arbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the ex-post sample-path return variability over a fixed time interval, (ii) the ex-ante expected volatility over a fixed time interval, and (iii) the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discrete-time ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete- and continuous-time stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recently-popularized realized volatility measures for (non-trivial) fixed-length time intervals.
The fine structure of asset returns: an empirical investigation
We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and variation. Empirical investigations of time series indicate that index dynamics are devoid of a diffusion component, which may be present in the dynamics of individual stocks. This leads to the conjecture, confirmed on options data, that the risk-neutral process should be free of a diffusion component. We conclude that the statistical and risk-neutral processes for equity prices are pure jump processes of infinite activity and finite variation
Pricing average price advertising options when underlying spot market prices are discontinuous
Advertising options have been recently studied as a special type of
guaranteed contracts in online advertising, which are an alternative sales
mechanism to real-time auctions. An advertising option is a contract which
gives its buyer a right but not obligation to enter into transactions to
purchase page views or link clicks at one or multiple pre-specified prices in a
specific future period. Different from typical guaranteed contracts, the option
buyer pays a lower upfront fee but can have greater flexibility and more
control of advertising. Many studies on advertising options so far have been
restricted to the situations where the option payoff is determined by the
underlying spot market price at a specific time point and the price evolution
over time is assumed to be continuous. The former leads to a biased calculation
of option payoff and the latter is invalid empirically for many online
advertising slots. This paper addresses these two limitations by proposing a
new advertising option pricing framework. First, the option payoff is
calculated based on an average price over a specific future period. Therefore,
the option becomes path-dependent. The average price is measured by the power
mean, which contains several existing option payoff functions as its special
cases. Second, jump-diffusion stochastic models are used to describe the
movement of the underlying spot market price, which incorporate several
important statistical properties including jumps and spikes, non-normality, and
absence of autocorrelations. A general option pricing algorithm is obtained
based on Monte Carlo simulation. In addition, an explicit pricing formula is
derived for the case when the option payoff is based on the geometric mean.
This pricing formula is also a generalized version of several other option
pricing models discussed in related studies.Comment: IEEE Transactions on Knowledge and Data Engineering, 201
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