Delta normal and delta gamma normal approximation in risk measurement of portfolio consisted of option and stock

Sulistianingsih, Evy; Rosadi, Dedi; Abdurakhman, Abdurakhman

doi:10.1063/1.5139181

Cited by 1 publication

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first assumption is that changes in option pricing and stock returns have a nonlinear relationship. The second assumption is that the stock returns that underlying the options are assumed to be normally distributed with mean zero (𝐸[∆𝑆] = 0) and variance 𝜎 2 (𝑉𝑎𝑟[∆𝑆] = 𝜎 2 ) (Sulistianingsih et al, 2019).…”

Section: Delta Gamma Normal Var (Dgn Var)mentioning

confidence: 99%

“…Based on Equation (4), the mean and variance obtained for a holding period (ℎ𝑝) in Equation ( 5) and Equation ( 6) are as follows (Dowd, 2007;Sulistianingsih et al, 2019):…”

Section: Delta Gamma Normal Var (Dgn Var)mentioning

confidence: 99%

“…Then, substitute the mean and variance of the option in the general estimate of VaR to obtain the DGN VaR for stock options as follows (Sulistianingsih et al, 2019).…”

Section: Delta Gamma Normal Var (Dgn Var)mentioning

confidence: 99%

“…Unlike stocks, which depend linearly on market risk factors, options have a nonlinear dependence on these factors. Delta Normal VaR (DN VaR) and Delta Gamma Normal VaR (DGN VaR) have been developed using the Taylor Polynomial concept to approximate the return value of the stocks underlying the call option (Sulistianingsih et al, 2019). DN VaR uses a first-order Taylor Polynomial, while DGN VaR uses a second-order Taylor Polynomial (Date & Bustreo, 2016).…”

Section: A Introductionmentioning

confidence: 99%

“…They found that the DGN VaR method outperformed the DN VaR method in terms of accuracy and computational efficiency. Sulistianingsih et al (2019) used a portfolio consisting of one stock (Exxon Mobile Corporation (XOM)) and two options from JD.com, Inc (JD) and Eni. S.p.A. (E).…”

Section: A Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Application of Delta Gamma Normal Value at Risk to Measure the Risk in the Call Option of Stock

Astuti,

Sulistianingsih,

Martha

et al. 2024

JTAM

View full text Add to dashboard Cite

Call options of stock have a nonlinear dependence on market risk factors, thus encouraging the development of a method capable of measuring the risk of call option of stock, namely the Delta Gamma Normal Value at Risk (DGN VaR) method. The DGN VaR method can provide a more accurate VaR estimate than Delta Normal VaR (DN VaR) because of the Delta and Gamma sensitivity measures in the formula. The DGN VaR method uses the second-order Taylor Polynomial approach to approximate the return of stock price underlying the call option. This research applies the DGN VaR method to analyze the risk of call options of Atlassian Corporation (TEAM) and MicroStrategy Incorporated (MSTR). Both companies operate in the technology sector and are among the top 100 largest software companies based on market capitalization for the analysis period September 21, 2022 to September 21, 2023. The analyzed options in this research consist of in-the-money and out-of-the-money options with several strike prices (K). For in-the-money options, the strike prices are $105, $110, and $115 for TEAM, and $150, $160, and $170 for MSTR, while for out-of-the-money options, the strike prices are $190, $195, and $200 for TEAM, and $330, $340, and $350 for MSTR with varying confidence levels of 80%, 90%, 95%, and 99%. Based on the results of the analysis, the DGN VaR for the analyzed in-the-money option has a greater value than the DGN VaR for the analyzed out-of-the-money option.

show abstract

Section: Delta Gamma Normal Var (Dgn Var)mentioning

confidence: 99%

“…Based on Equation (4), the mean and variance obtained for a holding period (ℎ𝑝) in Equation ( 5) and Equation ( 6) are as follows (Dowd, 2007;Sulistianingsih et al, 2019):…”

Section: Delta Gamma Normal Var (Dgn Var)mentioning

confidence: 99%

“…Then, substitute the mean and variance of the option in the general estimate of VaR to obtain the DGN VaR for stock options as follows (Sulistianingsih et al, 2019).…”

Section: Delta Gamma Normal Var (Dgn Var)mentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

Section: A Introductionmentioning

confidence: 99%

See 3 more Smart Citations