Suddenly its not just comparing the current price to the price of the contract, or is it?

Sure it is. Suppose you bought 100 option contracts (each for 100 shares) and paid a $1 per share premium ($10,000 total). Now those options are trading for $1.50 per share. You have an unrealized $0.50 gain per share, or $5,000. The $10,000 in options you bought are now worth $15,000. It holds whether they were bought to open or close a position, or whether they are puts or calls. The only difference is whether you bought or sold the options (the match is just reversed for selling an option).

But lets say we have an Option, where the payoff is max(St-K, c0) where ct is the market price. What do you do then?

Your current, unrealized P&L is different than the payoff. The payoff only happens at maturity. The current P&L is based on current market prices, just like stock. Option prices all have a "time premium" making them worth more than their payoff (intrinsic) value prior to maturity.

Suddenly its not just comparing the current price to the price of the contract, or is it?

Sure it is. Suppose you bought 100 option contracts (each for 100 shares) and paid a $1 per share premium ($10,000 total). Now those options are trading for $1.50 per share. You have an unrealized $0.50 gain per share, or $5,000. The $10,000 in options you bought are now worth $15,000. It holds whether they were bought to open or close a position, or whether they are puts or calls. The only difference is whether you bought or sold the options (the arithmetic is just reversed for selling an option).

But lets say we have an Option, where the payoff is max(St-K, c0) where ct is the market price. What do you do then?

Your current, unrealized P&L is different than the payoff. The payoff only happens at maturity. The current P&L is based on current market prices, just like stock. Option prices all have a "time premium" making them worth more than their payoff (intrinsic) value prior to maturity.

Suddenly its not just comparing the current price to the price of the contract, or is it?

Sure it is. Suppose you bought 100 option contracts (each for 100 shares) and paid a $1 per share premium ($10,000 total). Now those options are trading for $1.50 per share. You have an unrealized $0.50 loss per share, or $5,000. It holds whether they were bought to open or close a position, or whether they are puts or calls. The only difference is whether you bought or sold the options (the match is just reversed for selling an option).

But lets say we have an Option, where the payoff is max(St-K, c0) where ct is the market price. What do you do then?

Your current, unrealized P&L is different than the payoff. The payoff only happens at maturity. The current P&L is based on current market prices, just like stock.

Suddenly its not just comparing the current price to the price of the contract, or is it?

Sure it is. Suppose you bought 100 option contracts (each for 100 shares) and paid a $1 per share premium ($10,000 total). Now those options are trading for $1.50 per share. You have an unrealized $0.50 gain per share, or $5,000. The $10,000 in options you bought are now worth $15,000. It holds whether they were bought to open or close a position, or whether they are puts or calls. The only difference is whether you bought or sold the options (the match is just reversed for selling an option).

But lets say we have an Option, where the payoff is max(St-K, c0) where ct is the market price. What do you do then?

Your current, unrealized P&L is different than the payoff. The payoff only happens at maturity. The current P&L is based on current market prices, just like stock. Option prices all have a "time premium" making them worth more than their payoff (intrinsic) value prior to maturity.