Sep 21 Paper A Q4 iii)

[sophieactrainee]

Hi,

I apologise for the amount of questions!

I had a question on iii) of Q4.

In ASET solution, it mentions the principle of arbitrage implies that the inequality found in ii) (V_T > S_T) must hold at all earlier times.

I don't get why this is the case? I.e. why does arbitrage free and V_T > S_T imply v_t > s_t for all t < T?

Thanks

 

[John Potter]

If a washing machine is absolutely guaranteed to be worth more than a dishwasher on Xmas day V_T > S_T

but, currently, the dishwasher is more expensive V_t < S_t

you would just sell the expensive dishwasher and buy the cheap washing machine - money to you now, S_t - V_t , which you can hide under the bed.

Then you just wait around (hand-washing dishes but, crucially, not clothes!) until Xmas day, before doing the reverse buy/sell - even more money V_T - S_T for you to stash under the bed. If you do this a gazillion times, you can buy all the washing machines in the world, which isn't allowed by the principle of no arbitrage.

It's the same with shares and derivatives - just you get to avoid rubbish jokes about dishes

Good luck!
John

 

[sophieactrainee]

If a washing machine is absolutely guaranteed to be worth more than a dishwasher on Xmas day V_T > S_T

but, currently, the dishwasher is more expensive V_t < S_t

you would just sell the expensive dishwasher and buy the cheap washing machine - money to you now, S_t - V_t , which you can hide under the bed.

Then you just wait around (hand-washing dishes but, crucially, not clothes!) until Xmas day, before doing the reverse buy/sell - even more money V_T - S_T for you to stash under the bed. If you do this a gazillion times, you can buy all the washing machines in the world, which isn't allowed by the principle of no arbitrage.

It's the same with shares and derivatives - just you get to avoid rubbish jokes about dishes

Good luck!
John

Thank you!