xiaokeai

can someone please advise on these two questions?

1. how gamma changes when volatility goes up?

2. if you have a dice and you can throw three times. every time when you get a number you can choose continue the game or get paid by the number you get. what is the best strategy, when to stop..... i said when you see a number greater than 3 you stop.... is it correct?

Thanks a lot

QuantHR

1, Volatility going down has the same effect as the passage of time does. The farther the drop, the faster time goes by, so the at-the-money gamma goes up and the others dwindle a bit.

2,这道题比较复杂，heard on the street书里好像有一道类似的，你看看，网上也有针对throw n times的策略，你搜索试试。

jxwahc

let me try.
1. The effect of vol goes up could be deemed as stock price moves closer to strike. So for vanilla call & put, gamma increases when vol goes up; while for vanilla digital, it depends.
2. I would assume that you are risk neutal. Then for the 1st round, if you see a number less than 5, you should choose to continue because its expected value is 161/36; for the 2nd round, if you see a number less than 4, you should choose to continue because its expected value is 3.5

xiaokeai

i think you are right on the second one. thanks