錦衣衞
2019-2-23 01:02:31
Yeah anything is better than nothing and they were looking for a PhD intern so I just applied. Also I’m in Melbourne so Sydney is close.
It will be a lot easier to find a full time role with an internship. Anyways They still haven’t sent me the official offer yet so just keep it under wraps and fingers crossed.
大家睇完上半part應該都仲記得 (change of) Wiener process dW_t ~ N(0,dt)
所以我地其實可以當change of wiener process係一粒follow normal distribution嘅random number咁睇
因為咁 個問題就簡化到點樣generate一粒follow normal distribution嘅random number?
或者換個角度問就係我地用電腦可以點喺一個normal distribution入面拎一粒sample出黎?
( 詳細點樣generate容後再講 因為我想連埋variance reduction去講 咁樣個脈絡會完整啲 )
咁假設我地真係寫到個programme 可以喺一個standard normal distribution裡面抽到任意咁多粒independent嘅sample出黎
i.e. 我地個programme generate到任意咁多粒independent嘅random number 而佢地全部follow N(0,1)
上面咁講係咪好長氣呢 所以通常我地會好似下面幅圖咁寫
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where i.i.d. = independent and identically distributed
咁其實我地已經處理到n條互相冇correlation嘅wiener processes嘅simulation
但係當我地加咗correlation入去嗰n條processes入面 真正嘅問題就出現
上面我地一路都係講緊in general n粒R.V.s 嘅case
首先我地簡化少少先 剩係consider兩粒 R.V.s , i.e. X_1 and X_2
然後再assume埋 X_1 , X_2 ~ N(0,1)
而佢地係jointly follow Bivariate Normal Distribution (with correlation ρ)
有咗上面堆assumption之後 我地就可以開始問真正關鍵嘅問題
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「究竟有冇辦法用 另外兩粒iid 嘅 standard normal R.V.s (i.e. Z_1 and Z_2) 去 generate到 X_1 同 X_2 出黎?」
換句話講即係問緊我地有冇辦法將個correlation structure塞入去 Z_1 , Z_2 入面令佢地變成 X_1 , X_2
錦衣衞
2019-2-24 19:11:51
By the way, in page20 you mentioned bond options being exotic. But I thought exotic means some kinda path dependent products as opposed to vanilla products?
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宇智波月巴
2019-2-24 19:30:37
I think in the current market, the word “exotic” indeed refers to products with some kind of path dependent payoff
But in a broader sense, it could also refer to uncommon products traded in the market in contrast to vanilla options
錦衣衞
2019-2-24 19:34:21
Indeed anything that’s not vanilla are called exotic. I’m just not sure if an European call on a bond is exotic. Coz the payoff of an European call is considered vanilla.
宇智波月巴
2019-2-24 19:36:56
Oh I see your point
Maybe the best way is not to classify it
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錦衣衞
2019-2-24 19:39:13
And usually exotic products are priced by Monte Carlo simulation.
By the way do you have a chat group? Telegram is not working I think.