Skip to main content
Top

2023 | OriginalPaper | Chapter

8. Options and Volatilities

Author : Ilia Bouchouev

Published in: Virtual Barrels

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter summarizes the main building blocks that make up the business of volatility trading. It starts by covering remarkable contributions of Louis Bachelier whose a century-old pricing formula is still being used by oil traders. The classical Black-Scholes-Merton framework of option replication is then presented in a more general setting of diffusion processes. We highlight the importance of distinguishing between three commonly used types of volatility: local volatility, realized volatility, and implied volatility.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Footnotes
1
Bachelier (1900).
 
2
Black and Scholes (1973), and Merton (1973).
 
3
Some energy commodities, such as natural gas or power prices, are more susceptible to large short-term spikes where diffusions are often combined with jump processes, but this modeling paradigm is more complex as options can no longer be dynamically replicated with futures. We discuss some limitations of diffusions in Chap. 12.
 
4
Black (1976).
 
5
For the type of options studied by Bachelier, the discounting was not necessary as the option premium was netted against settlement at expiry. As a result, in his original derivation the interest rate was ignored. We will explain shortly why a similar assumption can be made for pricing many oil options. The discounting factor brings in an additional time dependency resulting from the present value of money, rather than from the evolution of the variance.
 
6
Greeks are discussed in many standard derivatives textbooks, such as Alexander (2008) and Hull (2018). For their practical interpretation, see also Leoni (2014).
 
7
Vega is not a letter of a Greek alphabet but it was adopted by option traders for its phonetic similarity.
 
8
See, for example, Wilmott et al. (1993).
 
9
Barone-Adesi and Whaley (1987).
 
10
For example, if daily prices are used then realized volatility is the standard deviation of returns multiplied by \( \sqrt{250} \) given approximately 250 trading days in a year, and for weekly prices, it is multiplied by \( \sqrt{52} \).
 
11
See Samuelson (1965).
 
Literature
go back to reference Alexander, C. (2008). Market risk analysis, Vol. III: Pricing, hedging and trading financial instruments. Wiley. Alexander, C. (2008). Market risk analysis, Vol. III: Pricing, hedging and trading financial instruments. Wiley.
go back to reference Bachelier, L. (1900). Théorie de la Spéculation, Annales scientifiques de l’Êcole Normale Supêrieure, Serie 3, 17, 21–86. Bachelier, L. (1900). Théorie de la Spéculation, Annales scientifiques de l’Êcole Normale Supêrieure, Serie 3, 17, 21–86.
go back to reference Barone-Adesi, G., & Whaley, R. E. (1987). Efficient analytic approximation of American option values. Journal of Finance, 42(2), 301–320.CrossRef Barone-Adesi, G., & Whaley, R. E. (1987). Efficient analytic approximation of American option values. Journal of Finance, 42(2), 301–320.CrossRef
go back to reference Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1/2), 167–179.CrossRef Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1/2), 167–179.CrossRef
go back to reference Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3), 637–654.MathSciNetCrossRefMATH Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3), 637–654.MathSciNetCrossRefMATH
go back to reference Hull, J. C. (2018). Options, futures, and other derivatives (10th ed.). Pearson.MATH Hull, J. C. (2018). Options, futures, and other derivatives (10th ed.). Pearson.MATH
go back to reference Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6(2), 41–49. Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6(2), 41–49.
go back to reference Wilmott, P., Dewynne, J., & Howison, S. (1993). Option pricing: Mathematical models and computation. Oxford Financial Press.MATH Wilmott, P., Dewynne, J., & Howison, S. (1993). Option pricing: Mathematical models and computation. Oxford Financial Press.MATH
Metadata
Title
Options and Volatilities
Author
Ilia Bouchouev
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-36151-7_8