FORWARD AND FUTURE IMPLIED VOLATILITY

2011 ◽  
Vol 14 (03) ◽  
pp. 407-432 ◽  
Author(s):  
PAUL GLASSERMAN ◽  
QI WU
Keyword(s):  
Implied Volatility ◽  
Transition Density ◽  
Option Prices ◽  
Piecewise Constant ◽  
Model Based ◽  
Model Free ◽  
Out Of Sample ◽  
Sabr Model ◽  
Using Data ◽  
Better Than

We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asymptotic expansion of the bivariate transition density in Wu (forthcoming) allows calibration of the SABR model with piecewise constant parameters and calculation of forward volatility. We then investigate empirically whether current option prices at multiple maturities contain useful information in predicting future option prices and future implied volatility. We undertake this investigation using data on options on the euro-dollar, sterling-dollar, and dollar-yen exchange rates. We find that prices across maturities do indeed have predictive value. Moreover, we find that model-based forward volatility extracts this predicative information better than a standard "model-free" measure of forward volatility and better than spot implied volatility. The enhancement to out-of-sample forecasting accuracy gained from model-based forward volatility is greatest at longer forecasting horizons.

An Empirical Research on the Informational Efficiency of Model Free Implied Volatility

2008 ◽  
Vol 16 (2) ◽  
pp. 67-94
Author(s):  
Byung Kun Rhee ◽  
Sang Won Hwang
Keyword(s):  
Implied Volatility ◽  
Realized Volatility ◽  
Informational Efficiency ◽  
Option Prices ◽  
Index Options ◽  
Model Free ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Korean Market ◽  
Better Than

Black-Scholes Imolied volatility (8SIV) has a few drawbacks. One is that the model Is not much successful in fitting the option prices. and It Is n야 guaranteed the model is correct one. Second. the usual tradition in using the BSIV is that only at-the-money Options are used. It is well-known that IV's of In-the-money or Qut-of-the-money ootions are much different from those estimated from near-the-money options. In this regard, a new model is confronted with Korean market data. Brittenxmes and Neuberger (2000) derive a formula for volatility which is a function of option prices‘ Since the formula is derived without using any option pricing model. volatility estimated from the formula is called model-tree implied volatillty (MFIV). MFIV overcomes the two drawbacks of BSIV. Jiang and Tian (2005) show that. with the S&P index Options (SPX), MFIV is suoerlor to historical volatility (HV) or BSIV in forecasting the future volatllity. In KOSPI 200 index options, when the forecasting performances are compared, MFIV is better than any other estimated volatilities. The hypothesis that MFIV contains all informations for realized volatility and the other volatilities are redundant is oot rejected in any cases.

scholarly journals EXACT PRICING AND LARGE-TIME ASYMPTOTICS FOR THE MODIFIED SABR MODEL AND THE BROWNIAN EXPONENTIAL FUNCTIONAL

2011 ◽  
Vol 14 (04) ◽  
pp. 559-578 ◽  
Author(s):  
MARTIN FORDE
Keyword(s):  
Stock Price ◽  
Implied Volatility ◽  
Large Time ◽  
Transition Density ◽  
Closed Form Expression ◽  
Modified Model ◽  
Exponential Functional ◽  
Price Distribution ◽  
Zero Correlation ◽  
Sabr Model

We derive a closed-form expression for the stock price density under the modified SABR model [see section 2.4 in Islah (2009)] with zero correlation, for β = 1 and β < 1, using the known density for the Brownian exponential functional for μ = 0 given in Matsumoto and Yor (2005), and then reversing the order of integration using Fubini's theorem. We then derive a large-time asymptotic expansion for the Brownian exponential functional for μ = 0, and we use this to characterize the large-time behaviour of the stock price distribution for the modified SABR model; the asymptotic stock price "density" is just the transition density p(t, S0, S) for the CEV process, integrated over the large-time asymptotic "density" [Formula: see text] associated with the Brownian exponential functional (re-scaled), as we might expect. We also compute the large-time asymptotic behaviour for the price of a call option, and we show precisely how the implied volatility tends to zero as the maturity tends to infinity, for β = 1 and β < 1. These results are shown to be consistent with the general large-time asymptotic estimate for implied variance given in Tehranchi (2009). The modified SABR model is significantly more tractable than the standard SABR model. Moreover, the integrated variance for the modified model is infinite a.s. as t → ∞, in contrast to the standard SABR model, so in this sense the modified model is also more realistic.

scholarly journals Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 30
Author(s):  
Fabien Le Floc’h ◽  
Cornelis Oosterlee
Keyword(s):  
Implied Volatility ◽  
Initial Guess ◽  
Stochastic Collocation ◽  
Option Prices ◽  
Spline Collocation ◽  
Model Free ◽  
Free Interpolation ◽  
Collocation Technique ◽  
Interpolation Technique ◽  
The Stability

This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how to smooth out the market quotes, and choose a proper initial guess. The technique is then applied to concrete market options and the stability of the different approaches is analyzed. Finally, we consider a challenging example where convex spline interpolations lead to oscillations in the implied volatility and compare the spline collocation results with those obtained through arbitrage-free interpolation technique of Andreasen and Huge.

Representation, abstraction, and simple-minded sophisticates

2020 ◽  
Vol 43 ◽  
Author(s):  
Peter Dayan
Keyword(s):  
Decision Theory ◽  
Predictive Coding ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Model Based ◽  
Model Free

Abstract Bayesian decision theory provides a simple formal elucidation of some of the ways that representation and representational abstraction are involved with, and exploit, both prediction and its rather distant cousin, predictive coding. Both model-free and model-based methods are involved.

Model-Based and Model-Free Social Cognition

2019 ◽  
Author(s):  
Leor M Hackel ◽  
Jeffrey Jordan Berg ◽  
Björn Lindström ◽  
David Amodio
Keyword(s):  
Reinforcement Learning ◽  
Social Cognition ◽  
Learning Strategies ◽  
Memory Systems ◽  
Learning Task ◽  
Financial Advisors ◽  
Model Based ◽  
Model Free ◽  
Systems Model ◽  
Task Assessment

Do habits play a role in our social impressions? To investigate the contribution of habits to the formation of social attitudes, we examined the roles of model-free and model-based reinforcement learning in social interactions—computations linked in past work to habit and planning, respectively. Participants in this study learned about novel individuals in a sequential reinforcement learning paradigm, choosing financial advisors who led them to high- or low-paying stocks. Results indicated that participants relied on both model-based and model-free learning, such that each independently predicted choice during the learning task and self-reported liking in a post-task assessment. Specifically, participants liked advisors who could provide large future rewards as well as advisors who had provided them with large rewards in the past. Moreover, participants varied in their use of model-based and model-free learning strategies, and this individual difference influenced the way in which learning related to self-reported attitudes: among participants who relied more on model-free learning, model-free social learning related more to post-task attitudes. We discuss implications for attitudes, trait impressions, and social behavior, as well as the role of habits in a memory systems model of social cognition.

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