option price = intrinsic value + time value where intrinsic value is the defined generally as difference between the underlying asset price and strike price (order depending on the type of option of course).

In the quantitative pricing models only the difference between the underlying price and strike seem to be modeled. For example the price of a call assuming no arbitrage possible is presented as

$V_{(0)}=\bar{V_n}=E^*[\bar{V_n}]=E^*[\frac{(S_n^j-K)}{S_n^0}]$

how the time value is defined/reflected here?

option price = intrinsic value + time value where intrinsic value (in other words payoff at N) is defined generally as difference between the underlying asset price and strike price (order depending on the type of the option of course).

In the quantitative pricing models only the difference between the underlying price and strike seem to be modeled. For example the price of a call assuming no arbitrage possible is presented as

$V_{(0)}=\bar{V_n}=E^*[\bar{V_n}]=E^*[\frac{(S_n^j-K)}{S_n^0}]$

how the time value is defined/reflected here?