A Black–Scholes user's guide to the Bachelier model

Choi, Jaehyuk; Kwak, Minsuk; Tee, Chyng Wen; Wang, Yumeng

doi:10.1002/fut.22315

Cited by 9 publications

(4 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This model stimulated future stock prices of TSLA based on Equation (9). These 1000 stimulations of TSLA's future stock price are used to calculate respective option price.…”

Section: Resultsmentioning

confidence: 99%

“…Instead of using Equation (5), we price the chooser option based on the simpler but more straightforward method, Equation (9). The basic concept of a chooser lies in individual call and put options, with an additional right to choose whether it is a call or a put at a specific time 𝑡 1 .…”

Section: Chooser Option Pricing Methods Based On Black-scholes Modelmentioning

confidence: 99%

“…The formular of the model is derived by multiplying the stock price by the cumulative standard normal probability distribution function. Besides, plenty of empirical studies have been conducted on the Black-Scholes option pricing model in the developed markets [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chooser Option Pricing of Tesla in Terms of Monte-Carlo Simulations

Li¹,

Liu²

2023

Proceedings of the International Conference on Financial Innovation, FinTech and Information Technology, FFIT 2022, October 28-

View full text Add to dashboard Cite

In option trading, how to buy, how much to buy and when to trade all affect the ultimate interests of traders. However, the use of appropriate models and analysis methods can help traders predict the changes in stock prices and make corresponding countermeasures. This paper will rely on the historical stock price data of Tesla, analyze it according to black-Scholes model and Monte-Carlo method, and estimate the possible changes of stock price.

show abstract

“…This model stimulated future stock prices of TSLA based on Equation (9). These 1000 stimulations of TSLA's future stock price are used to calculate respective option price.…”

Section: Resultsmentioning

confidence: 99%

Section: Chooser Option Pricing Methods Based On Black-scholes Modelmentioning

confidence: 99%

See 1 more Smart Citation

Chooser Option Pricing of Tesla in Terms of Monte-Carlo Simulations

Li¹,

Liu²

2023

Proceedings of the International Conference on Financial Innovation, FinTech and Information Technology, FFIT 2022, October 28-

View full text Add to dashboard Cite

show abstract

“…A normal density corresponds to the Bachelier model, which has mostly been ignored for a long time, but regained attention in the context of negative interest rates and negative prices for oil-futures. 29,30 Using the forward price F of the underlying asset, the strike of the option K, the normal volatility σ and the time to expiry τ , we define the moneyness m of an option in the following way:…”

Section: A Normal Densitymentioning

confidence: 99%

Sparse modeling approach to the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities

Guterding¹

2022

Preprint

View full text Add to dashboard Cite

We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as a system of linear equations. We show that the kernel matrix of this system is in general ill-conditioned, so that it can not be solved for the discretized density using a naive approach. Instead, we construct a sparse model for the kernel matrix using the singular value decomposition (SVD), which allows us not only to systematically improve the condition number of the kernel matrix, but also determines the computational effort and accuracy of our method. In order to allow for the treatment of realistic inputs that may contain arbitrage, we reformulate the system of linear equations as an optimization problem, in which the SVD-transformed density minimizes the error between the input prices and the arbitrage-free prices generated by our method. To further stabilize the method in the presence of noisy input prices or arbitrage, we apply an L1-regularization to the SVD-transformed density. Our approach, which is inspired by recent progress in theoretical physics, offers a flexible and efficient framework for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, without the need to explicitly specify a stochastic process, expansion basis functions or any other kind of model. We demonstrate the capabilities of our method on a number of artificial and realistic test cases.

show abstract

An empirical test of auction methods in the primary market of sovereign debt

Jiménez

Mochón²

2022

Spanish Journal of Finance and Accounting / Revista Española de

View full text Add to dashboard Cite

A Black–Scholes user's guide to the Bachelier model

Cited by 9 publications

References 55 publications

Chooser Option Pricing of Tesla in Terms of Monte-Carlo Simulations

Chooser Option Pricing of Tesla in Terms of Monte-Carlo Simulations

Sparse modeling approach to the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities

An empirical test of auction methods in the primary market of sovereign debt

Contact Info

Product

Resources

About