# What is the P&L

If we sell a call option on a stock with a volatility of 16%. Theta is worth 100€/day. Let's assume that the spot moves by 2% in one day. What is the P&L ?

Thank you for the help

Can’t be calculated precisely from the information given, but we can make an approximation: -first, assume that you delta hedged your call so we start with a delta neutral portfolio -second, note that 16% vol is equivalent to a daily move of 16%/sqrt(252)= about 1% per day

• we may therefore estimate that a move of 1% would balance the negative gamma versus the theta. Hence , the negative gamma p/l of a 1% move is -100.
• Since gamma is quadratic, the gamma p/l of a 2% move should be -400.
• Hence the overall p/l = theta gain minus gamma loss = 100-400= a loss of 300 dollars.
• Thank for your answer ! Why can u suppose that a move of 1% would balance the negative gamma versus the theta ? I don't see why this assumption would be logical or narutal ? Commented Apr 22 at 16:25
• The fundamental equation of option pricing, aka the Black Scholes equation, basically says that time decay equals Expected gamma p/l. The move of 1% daily is the expected move, given that the option is priced at 16% annual volatility.
– dm63
Commented Apr 22 at 16:42
• I’m being rather loose with the details, apologies to the quants
– dm63
Commented Apr 22 at 16:43
• Thank you ! One more question, i don't understand where do we use that the vol is 1% per day ? And why did you choose to work with gamma instead of, for example, vega? Commented Apr 22 at 17:44
• We use that the gamma p/l of a 1% move is 100k, in order to calculate the gamma p/l of a 2% move. Second question we assumed implied vol did not move so there is no Vega p/l. Pls consult a basic options text.
– dm63
Commented Apr 23 at 9:32