Log Student’s<i>t</i>-distribution-based option sensitivities: Greeks for the Gosset formulae

Cassidy, Daniel T.; Hamp, Michael J.; Ouyed, Rachid

doi:10.1080/14697688.2012.744087

Cited by 9 publications

(11 citation statements)

References 14 publications

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“…When one uses a distribution with fat tails, the option pricing integral (2.2) would diverge since the exponential price term cannot be compensated with any power law decay. Bouchaud & Sornette (1994), Cassidy et al (2013) and McCauley et al (2007) provide explanation of such a problem. In this case, one has to find some remedy, such as truncating the distribution sharply like Cassidy et al (2010) have suggested, or using one with far part of the tail falling off exponentially as is proposed by Moriconi (2007) and Cassidy (2012).…”

Section: Fair Price Of European Style Optionmentioning

confidence: 99%

“…where x max is the point where the distribution is truncated. Once one has fully determined the option price formula (2.7), when Student's t-distribution is used for log return, the Greeks can be easily calculated as was shown by Cassidy et al (2013). Note that the same convergence problem would not appear for put options, which are characterized with nonzero value at maturity when the stock price S is lower than the strike K. Hence, by averaging over the distribution of the returns on the underlying stock the current put option price is…”

Section: Fair Price Of European Style Optionmentioning

confidence: 99%

“…The resulting models for pricing options offer determination of the values for a whole range of strikes and maturities by using a single parameter. In the second contribution, Cassidy et al (2010) and Cassidy et al (2013) apply truncated Student's t-distribution directly, and provide an analysis for the position of the truncation point. Our valuation framework is primarily driven by the empirical observations rather than aiming to provide a strong analytical theory.…”

Section: Introductionmentioning

confidence: 99%

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Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

Basnarkov

Stojkoski

Utkovski

et al. 2019

Int. J. Theor. Appl. Finan.

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A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European options. Probability density functions of log returns for different periods are conveniently taken to be convolutions of the Student's t-distribution with three degrees of freedom. The supports of these distributions are truncated in order to obtain finite values for the options. Within this framework, options with different strikes and maturities for one stock rely on a single parameter -the standard deviation of the Student's t-distribution for unit period. We provide a study which shows that the distribution support width has weak influence on the option prices for certain range of values of the width. It is furthermore shown that such family of truncated distributions approximately satisfies the no-arbitrage principle and the put-call parity. The relevance of the pricing procedure is empirically verified by obtaining remarkably good match of the numerically computed values by our scheme to real market data.

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Section: Fair Price Of European Style Optionmentioning

confidence: 99%

Section: Fair Price Of European Style Optionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

Basnarkov

Stojkoski

Utkovski

et al. 2019

Int. J. Theor. Appl. Finan.

View full text Add to dashboard Cite

show abstract

“…This model is realistic in that it allows for a finite supply of money to be saturated by the net rate of transactions and does not require truncation or capping [8] [9] [13] [14], or modification of the distribution of returns [10] [11] [12] to avoid very large and unobserved stock prices. This homogeneously saturated model, which borrows from laser physics [15], will have widely spread repercussions, most importantly for the Black-Scholes formula for option pricing, which will be investigated in future work.…”

Section: Discussionmentioning

confidence: 99%

Extended Model of Stock Price Behaviour

Koning¹,

Cassidy²,

Ouyed³

2018

JMF

Self Cite

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We have developed an extended model for stock price behaviour that is able to accommodate fat-tailed distributions with support as large as [ ] , −∞ ∞ . The "homogeneously saturated" (HS) model avoids exponential price changes for large fluctuations by means of a saturation parameter. In the limit where the saturation parameter is zero, the standard model of stock price behaviour (i.e., geometric Brownian motion) is recovered. We compare simulated stock price series generated for both the standard and HS model for the DJIA and five random stocks from the NYSE and NASDAQ exchanges. We find that in all cases, the HS model provides a better fit to the observed price series than the standard model. This has implications to many areas of finance including the Black-Scholes formula for option pricing.

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“…Jie neturi vertės, pasibaigus terminui. Jeigu, pavyzdžiui, theta lygi 0,07, likus vienai dienai mažiau iki termino pabaigos, pasirinkimo sandorio kaina sumažės 0,07 Eur (Cassidy et al, 2013).…”

Section: Graikiškosios Raidės Vertinant Pasirinkimo Sandorių Kainos Junclassified

Assessment of Option Price Volatility

Sodaunykaitė

Martinkutė-Kaulienė

2020

Science - Future of Lithuania

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Financial derivatives are becoming increasingly popular on a daily basis. As markets become more unpredictable, companies and individual investors are increasingly using these tools to manage risk, leverage, and increase investment returns. The most important aspect of any contract is the contract price, as the financial result of the contract depends on the price. Also for an options. In each case, the option price depends on many factors that are difficult to define and predict in advance. The price sensitivity of the option allows you to determine where and on what the option price depends. Knowing this, the investor can manage the risk of the options. The purpose of the article is to assess the sensitivity of different options to market factors based on scientific literature and real market data. The study uses the Black-Scholes option pricing model, calculating and analyzing the value of Greek letters for the determination and valuation of transaction price sensitivity. The study showed that the most sensitive to changes in the underlying asset price, volatility and risk-free interest rate is the price of the currency option, and the price of the gold option is most sensitive over time (although in theory, gold retains its value in the long run). Knowing which components a particular option is sensitive to and capable of predicting changes in those components, you can predict changes in the option price and avoid additional risk.

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Log Student’st-distribution-based option sensitivities: Greeks for the Gosset formulae

Cited by 9 publications

References 14 publications

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

Option Pricing With Heavy-Tailed Distributions of Logarithmic Returns

Extended Model of Stock Price Behaviour

Assessment of Option Price Volatility

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