Quantitative Finance / Q-Fin.CP

All posts under category "Quantitative Finance / Q-Fin.CP"

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Financial Rogue Waves Appearing in the Coupled Nonlinear Volatility and Option Pricing Model

Financial Rogue Waves Appearing in the Coupled Nonlinear Volatility and Option Pricing Model

์ด ๋…ผ๋ฌธ์€ ๋น„์„ ํ˜• ๊ณผํ•™์—์„œ ์ค‘์š”ํ•œ ๊ฐœ๋…์ธ ํ”„๋ฆฌํฌ ํŒŒ๋„๋ฅผ ๊ธˆ์œต ์‹œ์žฅ์— ์ ์šฉํ•˜์—ฌ ์ƒˆ๋กœ์šด ๋ชจ๋ธ์„ ์ œ์‹œํ•œ๋‹ค. ํ”„๋ฆฌํฌ ํŒŒ๋„๋Š” ํ•ด์–‘ํ•™, ๊ด‘ํ•™ ๋“ฑ ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์—์„œ ์—ฐ๊ตฌ๋˜์—ˆ์œผ๋ฉฐ, ์ด ํ˜„์ƒ์˜ ํŠน์ง•์€ ๊ทน๋‹จ์ ์ธ ์‚ฌ๊ฑด์ด ๋ฐœ์ƒํ•  ๋•Œ ๋‚˜ํƒ€๋‚˜๋Š” ๊ฑฐ๋Œ€ํ•œ ํŒŒ๋„์ด๋‹ค. ๋…ผ๋ฌธ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ๊ฐœ๋…์„ ๊ธˆ์œต ์‹œ์žฅ์— ์ ์šฉํ•˜์—ฌ ๋ณ€๋™์„ฑ๊ณผ ์˜ต์…˜ ๊ฐ€๊ฒฉ ๊ฐ„์˜ ์ƒํ˜ธ์ž‘์šฉ์„ ๋ถ„์„ํ•˜๊ณ , ์ด๋ฅผ ํ†ตํ•ด ๊ธˆ์œต ์œ„๊ธฐ์™€ ๊ฐ™์€ ๊ทน๋‹จ์ ์ธ ์‚ฌ๊ฑด์„ ์„ค๋ช…ํ•˜๋ ค๊ณ  ํ•œ๋‹ค. 1. ํ”„๋ฆฌํฌ ํŒŒ๋„ ํ˜„์ƒ ํ”„๋ฆฌํฌ ํŒŒ๋„๋Š” ๋น„์„ ํ˜• ๊ณผํ•™์—์„œ ์ค‘์š”ํ•œ ๊ฐœ๋…์œผ๋กœ, ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์—์„œ ์—ฐ๊ตฌ๋˜์—ˆ๋‹ค. ์ด ๋…ผ๋ฌธ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ํ”„๋ฆฌํฌ ํŒŒ๋„์˜ ํŠน์„ฑ์„ ๊ธˆ

Nonlinear Sciences Quantitative Finance Model
Computation of copulas by Fourier methods

Computation of copulas by Fourier methods

์ด ๋…ผ๋ฌธ์€ ๋‹ค์ฐจ์› ๋žœ๋ค ๋ณ€์ˆ˜์˜ ์•”์‹œ์  ์ปคํ”Œ๋ผ ํ‘œํ˜„์— ๋Œ€ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ๋ฒ•์„ ์ œ์•ˆํ•˜๋ฉฐ, ํŠนํžˆ ํ‘ธ๋ฆฌ์— ๋ฐฉ๋ฒ•์„ ํ™œ์šฉํ•œ ๊ณ„์‚ฐ ๊ธฐ๋ฒ•์„ ์†Œ๊ฐœํ•œ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๋ฌด์ž‘์œ„ ๋ณ€์ˆ˜ ๊ฐ„์˜ ์˜์กด์„ฑ ๊ตฌ์กฐ๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ๋ฌ˜์‚ฌํ•˜๋Š” ๋ฐ ์ค‘์ ์„ ๋‘๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๋™์  ๊ณผ์ •์—์„œ ๋ฐœ์ƒํ•˜๋Š” ๋ณต์žกํ•œ ์ƒํ˜ธ ์ž‘์šฉ์„ ์ดํ•ดํ•˜๊ณ  ๋ถ„์„ํ•  ์ˆ˜ ์žˆ๋Š” ๋„๊ตฌ๋ฅผ ์ œ๊ณตํ•œ๋‹ค. 1. ์ปคํ”Œ๋ผ์™€ ์˜์กด์„ฑ ๊ตฌ์กฐ ์ปคํ”Œ๋ผ๋Š” ๋ฌด์ž‘์œ„ ๋ณ€์ˆ˜ ๊ฐ„์˜ ์˜์กด์„ฑ์„ ์™„๋ฒฝํ•˜๊ฒŒ ๋ฌ˜์‚ฌํ•˜๋ฉฐ, ์Šคํด๋ผ๋ฅด์˜ ์ •๋ฆฌ๋ฅผ ํ†ตํ•ด ๊ณต๋™ ๋ถ„ํฌ์™€ ์ด๋ถ„ ๋ถ„ํฌ ์‚ฌ์ด์˜ ๊ด€๊ณ„๋ฅผ ์šฐ์•„ํ•˜๊ฒŒ ์—ฐ๊ฒฐํ•œ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ปคํ”Œ๋ผ๋Š” ๋™์  ๊ณผ์ •๊ณผ ์ž˜ ์–ด์šธ๋ฆฌ์ง€ ์•Š์œผ๋ฉฐ, ์˜ˆ๋ฅผ

Mathematics Quantitative Finance
Symmetries of the Black-Scholes equation

Symmetries of the Black-Scholes equation

: ๋ณธ ๋…ผ๋ฌธ์€ ๋ธ”๋ž™ ์‡ผ์Šค ๋ฐฉ์ •์‹์˜ ๋Œ€์ˆ˜๊ธฐํ•˜ํ•™์  ๊ตฌ์กฐ๋ฅผ ํƒ๊ตฌํ•˜๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๊ธˆ์œต์ˆ˜ํ•™์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š” ๋ฏธ๋ถ„๋ฐฉ์ •์‹์˜ ๋Œ€์นญ์„ฑ์„ ๋ถ„์„ํ•˜๊ณ ์ž ํ•ฉ๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๊ณ ์ „ ๋ฌผ๋ฆฌํ•™๊ณผ ์œ ํด๋ฆฌ๋“œ ์–‘์ž์—ญํ•™์—์„œ ์ด๋ฏธ ์ž…์ฆ๋œ ๋ฐฉ๋ฒ•๋ก ์„ ๊ธˆ์œต์ˆ˜ํ•™์— ์ ์šฉํ•˜๋ ค๋Š” ์‹œ๋„๋กœ, ๋ธ”๋ž™ ์‡ผ์Šค ๋ฐฉ์ •์‹์˜ ๊ตฌ์กฐ๋ฅผ ๋” ๊นŠ์ด ์ดํ•ดํ•˜๊ณ ์ž ํ•ฉ๋‹ˆ๋‹ค. ๋…ผ๋ฌธ์€ ๋จผ์ € ๋ธ”๋ž™ ์‡ผ์Šค ๋ฐฉ์ •์‹์˜ ์ผ๋ฐ˜์ ์ธ ํ‹€์„ ์„ค์ •ํ•œ ํ›„, ์ด๋ถ„์ˆ˜๋ฅผ ๊ฒฐ์ •ํ•˜๊ธฐ ์œ„ํ•ด ์—ด๋ฐฉ์ •์‹๊ณผ ์ž ์žฌํ•ญ ํ•ญ๋ชฉ์— ๋Œ€ํ•œ ์—ญ์—ด๋ฐฉ์ •์‹์˜ ๋ฐฉ๋ฒ•๋ก ์„ ์ ์šฉํ•ฉ๋‹ˆ๋‹ค. ์ด๋ฅผ ํ†ตํ•ด ๋ธ”๋ž™ ์‡ผ์Šค ๋ฐฉ์ •์‹์˜ ์›๋ž˜ ํ•ด๊ฒฐ ๋ฐฉ๋ฒ•์ด ์ž์—ฐ์Šค๋Ÿฝ๊ฒŒ ๋‚˜ํƒ€๋‚˜๋ฉฐ, ํŠนํžˆ r ฯƒยฒโ‚‚์™€

Quantitative Finance Mathematics

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