Your client would like to buy a digital call option. the digital call option pays the buyer in one years time (i.e at maturity )
- N=1m SGD, if the SGD USD spot rate at maturity is above a prescribed level k_0 and nothing otherwise
Risk management of this structure is done, via conservative replication, with a pair of call options of strikes $K_1$ and $K_2$, $K_2$ > K_1 and with a spread size $\Delta K =K_2-K_1>0$.
Question: From the seller point of view, how would you choose the strikes $K_1 , K_2$ and notionals $N_1,N_2$ (possibly negative) of these call options as a function of $K_0$, $\Delta K$, and $N$ in such a way that
1) you overestimate the actual amount paid to the client if the spot falls between $K_1$ and $K_2 $
2) and match exactly actual amount otherwise?
Anybody can help me with this, and if possible ,explain what is meant by conservative replication as well as how can the notionals be negative? It does not make sense that i am a seller of a call option and i give a negative payout?