Forums  > Pricing & Modelling  > Price-adjustment of the Black-Scholes delta and gamma  
     
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HJA24


Total Posts: 2
Joined: Apr 2020
 
Posted: 2020-04-30 08:32
Hi all,

A quanto option is a derivative with the underlying and strike price denominated in one currency, but the instrument itself is settled in another currency. An example of this Bitcoin-options that are settled in BTC but the spot and strike is expressed in dollar. This has consequences for the calculation of the greeks for these options.

The standard Black-Scholes delta measures the rate of change of the option price relative to the change of underlying price. BS gamma measures the rate of change of BS delta relative to the change of underlying price.

One of the exchanges adopts price-adjusted delta and price-adjusted gamma OKEX and argue that
PA delta measures the rate of change of the option price (in settlement currency) relative to the percentage change of the underlying price. PA gamma measures the rate of change of PA delta relative to the percentage change of the underlying price


According to the link the difference between the BS delta and the PA delta is the price of the option (in BTC). Following the below logic (with interest rate=0) I found the proof:




I am trying to figure out if there is also a similar relationship between BS gamma and PA gamma. Please help me out, I am lost

nikol


Total Posts: 1063
Joined: Jun 2005
 
Posted: 2020-04-30 14:53
> Please help me out, I am lost

I am lost too. 1+1 = 2.

HJA24


Total Posts: 2
Joined: Apr 2020
 
Posted: 2020-04-30 17:05
thanks!
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