scholarly journals OPTION PRICING AND HEDGING WITH TEMPORAL CORRELATIONS

2002 ◽  
Vol 05 (03) ◽  
pp. 307-320 ◽  
Author(s):  
LORENZO CORNALBA ◽  
JEAN-PHILIPPE BOUCHAUD ◽  
MARC POTTERS
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
General Formula ◽  
Gaussian Processes ◽  
Risk Minimisation ◽  
Temporal Correlations ◽  
Hedging Strategies ◽  
Black Scholes ◽  
Non Gaussian

We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme with history-dependent hedging strategies, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black-Scholes formula holds with the volatility of the price increments calculated on the scale of the re-hedging. For non-Gaussian processes, further non trivial corrections to the "smile" are brought about by the correlations, even when the hedge is the Black-Scholes Δ-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.

Learning for infinitely divisible GARCH models in option pricing

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fumin Zhu ◽  
Michele Leonardo Bianchi ◽  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
Hengyu Wu
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Space Structure ◽  
Estimation Methods ◽  
Garch Models ◽  
Learning Approaches ◽  
Infinitely Divisible ◽  
Asymmetric Garch ◽  
Non Gaussian

AbstractThis paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

The Value of Insight

2020 ◽  
Vol 45 (4) ◽  
pp. 1193-1209
Author(s):  
Philip A. Ernst ◽  
L. C. G. Rogers
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
Stochastic Control ◽  
The Other ◽  
Control Problems ◽  
Bank Account ◽  
Stochastic Control Problems ◽  
Black Scholes ◽  
Log Price

An investor may invest in a riskless bank account and in a stock that is a standard Black–Scholes asset with occasional Gaussian jumps of the log price, as proposed by Merton [Merton RC ( 1976 ) Option pricing when underlying stock returns are discontinuous. J. Financial Econom. 3(1):125–144.]. It is well known how to solve the standard running consumption problem for this investor, which we take as a benchmark for comparing the performance of two different insiders, one who knows in advance of each jump exactly when the jump will happen, and the other who has information in advance of each jump about the size of the jump but no information about the time. These considerations give rise to two novel and concrete stochastic control problems. For each problem, rigorous verification proofs for optimality are presented.

scholarly journals Hedging options with an illiquid underlying and non-probabilistic option pricing in practice

2021 ◽  
Author(s):  
Nolan Nicholls
Keyword(s):  
Option Pricing ◽  
Probabilistic Model ◽  
European Options ◽  
The Third ◽  
Significant Potential ◽  
Pricing Options ◽  
Hedging Strategies ◽  
Black Scholes ◽  
Cross Hedging ◽  
Highly Correlated

We compare three different dynamic hedging strategies for the purchase or sale of a bundle of European options to profit from volatility arbitrage. The investor will "cross hedge" with a stock highly correlated with the untraded underlying. The first strategy maximizes terminal utility, the second minimizes the variance of the incremental profit, and the third is the adjusted Black-Scholes strategy. We note that the nature of cross hedging results in significant potential for losses. We study the robustness of the strategies to misspecification of parameters by the investor and find that the first two strategies are more robust to parameter misspecification. On a different subject, we then attempt to find profit opportunities by pricing options using a simple non-probabilistic model. We find a situation where an investor willing to take risks can profit, but a more cautious investor cannot. We also derive basic non-probabilistic volatility arbitrage results.

scholarly journals Hedging options with an illiquid underlying and non-probabilistic option pricing in practice

2021 ◽  
Author(s):  
Nolan Nicholls
Keyword(s):  
Option Pricing ◽  
Probabilistic Model ◽  
European Options ◽  
The Third ◽  
Significant Potential ◽  
Pricing Options ◽  
Hedging Strategies ◽  
Black Scholes ◽  
Cross Hedging ◽  
Highly Correlated

We compare three different dynamic hedging strategies for the purchase or sale of a bundle of European options to profit from volatility arbitrage. The investor will "cross hedge" with a stock highly correlated with the untraded underlying. The first strategy maximizes terminal utility, the second minimizes the variance of the incremental profit, and the third is the adjusted Black-Scholes strategy. We note that the nature of cross hedging results in significant potential for losses. We study the robustness of the strategies to misspecification of parameters by the investor and find that the first two strategies are more robust to parameter misspecification. On a different subject, we then attempt to find profit opportunities by pricing options using a simple non-probabilistic model. We find a situation where an investor willing to take risks can profit, but a more cautious investor cannot. We also derive basic non-probabilistic volatility arbitrage results.

scholarly journals Structure factors for generalized grey Browinian motion

2019 ◽  
Vol 22 (2) ◽  
pp. 396-411
Author(s):  
José L. da Silva ◽  
Ludwig Streit
Keyword(s):  
Gaussian Processes ◽  
Form Factors ◽  
Analytic Form ◽  
Debye Function ◽  
Asymptotic Decay ◽  
Structure Factors ◽  
Closed Analytic Form ◽  
Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

scholarly journals Option Pricing Driven by a Telegraph Process with Random Jumps

2012 ◽  
Vol 49 (3) ◽  
pp. 838-849 ◽  
Author(s):  
Oscar López ◽  
Nikita Ratanov
Keyword(s):  
Option Pricing ◽  
Financial Market ◽  
Option Prices ◽  
Martingale Measures ◽  
Market Models ◽  
Telegraph Process ◽  
Equivalent Martingale Measures ◽  
Hedging Strategies ◽  
Random Jumps ◽  
Equivalent Martingale

In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

scholarly journals Quanto Pricing beyond Black–Scholes

2021 ◽  
Vol 14 (3) ◽  
pp. 136
Author(s):  
Holger Fink ◽  
Stefan Mittnik
Keyword(s):  
Option Pricing ◽  
Goodness Of Fit ◽  
Calibration Procedure ◽  
Barrier Options ◽  
Pricing Models ◽  
Modeling Framework ◽  
Double Barrier ◽  
Parameter Stability ◽  
Comprehensive Data ◽  
Black Scholes

Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.

Sign in / Sign up

Export Citation Format

Share Document