Quantitative Finance / Q-Fin.ST

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Factorial Moments in Complex Systems

Factorial Moments in Complex Systems

: ๋ณธ ๋…ผ๋ฌธ์€ ํ•ต ๋ฐ˜์‘์—์„œ ์ตœ์ข… ์ƒํƒœ ์ž…์ž์˜ ๋‹ค์ค‘์„ฑ ๋ถ„ํฌ์™€ ์ƒํ˜ธ ๊ด€๊ณ„๋ฅผ ๋ถ„์„ํ•˜๋Š” ๋ฐ ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ๋‹ค. ์ด ์—ฐ๊ตฌ์—์„œ๋Š” ์‚ฌ์‹ค์  ์ˆœ๊ฐ„์ด๋ผ๋Š” ํ†ต๊ณ„ ๋„๊ตฌ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ์œ„์ƒ ๊ณต๊ฐ„ ๋‚ด์—์„œ ์ž…์ž ๊ฐ„์˜ ์ƒ๊ด€ ๊ด€๊ณ„์™€ ๋‹ค์ค‘์„ฑ ๋ถ„ํฌ๋ฅผ ์ž์„ธํžˆ ๋ถ„์„ํ•œ๋‹ค. 1. ํ•ต ๋ฐ˜์‘๊ณผ ์‚ฌ์‹ค์  ์ˆœ๊ฐ„ ํ•ต ๋ฐ˜์‘์—์„œ ์ตœ์ข… ์ƒํƒœ ์ž…์ž์˜ ๋‹ค์ค‘์„ฑ ๋ถ„ํฌ๋Š” ๊ณ ์—๋„ˆ์ง€ ๋ฌผ๋ฆฌํ•™์—์„œ ์ค‘์š”ํ•œ ์—ฐ๊ตฌ ์ฃผ์ œ์ด๋‹ค. ์ด ๋…ผ๋ฌธ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ๋ถ„ํฌ๋ฅผ ๋ถ„์„ํ•˜๊ธฐ ์œ„ํ•ด ์ •๊ทœํ™”๋œ ์‚ฌ์‹ค์  ์ˆœ๊ฐ„์ด๋ผ๋Š” ํ†ต๊ณ„ ๋„๊ตฌ๋ฅผ ์‚ฌ์šฉํ•œ๋‹ค. ์‚ฌ์‹ค์  ์ˆœ๊ฐ„์€ ํŠน์ • ์œ„์ƒ ๊ณต๊ฐ„ ์˜์—ญ ๋‚ด์—์„œ ์ธก์ •๋œ ์ž…์ž ์ˆ˜์˜ ๋ถ„ํฌ๋ฅผ ์ž์„ธํžˆ ๋ถ„์„ํ•˜๋Š” ๋ฐ ์œ ์šฉํ•˜๋‹ค

Quantitative Finance System
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Returns in futures markets and $nu=3$ t-distribution

๋ณธ ๋…ผ๋ฌธ์€ ๊ณ ์ฃผํŒŒ๋กœ ์ƒ˜ํ”Œ๋ง๋œ ๊ธˆ์œต ์‹œ๊ฐ„ ์‹œ๋ฆฌ์ฆˆ์˜ ๋กœ๊ทธ ๋ฐ˜ํ™˜ ํ™•๋ฅ  ๋ถ„ํฌ๋ฅผ ๋ถ„์„ํ•˜๊ณ , ์ด๋ฅผ ํ†ตํ•ด t ๋ถ„ํฌ๊ฐ€ ์‹ค์ œ ๋ฐ์ดํ„ฐ์™€ ์–ผ๋งˆ๋‚˜ ์ž˜ ์ผ์น˜ํ•˜๋Š”์ง€ ๊ฒ€์ฆํ•ฉ๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ์–‘์  ๊ธˆ์œต์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š” ๋กœ๊ทธ ๋ฐ˜ํ™˜ ๋ถ„ํฌ์— ๋Œ€ํ•œ ๊นŠ์ด ์žˆ๋Š” ์ดํ•ด๋ฅผ ์ œ๊ณตํ•˜๋ฉฐ, ํŠนํžˆ ฮฝ โ‰ˆ 3์ธ t ๋ถ„ํฌ์˜ ์ค‘์š”์„ฑ์„ ๊ฐ•์กฐํ•ฉ๋‹ˆ๋‹ค. 1. ๊ธˆ์œต ์‹œ๊ฐ„ ์‹œ๋ฆฌ์ฆˆ์™€ ๋กœ๊ทธ ๋ฐ˜ํ™˜ ๊ธˆ์œต ์‹œ๊ฐ„ ์‹œ๋ฆฌ์ฆˆ๋Š” ๊ฐ€๊ฒฉ ๋ณ€๋™์„ ๋‚˜ํƒ€๋‚ด๋ฉฐ, ์ด ๋ณ€๋™์€ ๋กœ๊ทธ ๋ฐ˜ํ™˜ x(t) log

Quantitative Finance

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