Hi, Please could I ask 1) What's the difference between a "replicating strategy" and a "replicating portfolio". Are they both the same with value (Phi_t, Psi_t) at time t? 2) We find a replicating portfolio (replicating strategy) to replicate the payoff of a derivative at time t or maturity T. But why are we doing this? Where would these methods be used in the actuarial industry and the wider world?
Hi 1. I’ll leave to someone who has access to the text that has prompted the question. 2. There are a number of reasons for wanting to do this. Some applications include: Valuation: insurers may write contracts whose payoff profile is identical to (say) holding stock and a derivative. By no arbitrage principles, the values must be the same. It can be quicker / easier to use these prices to value the contract than spending time developing (complex) valuation models. Risk management: a company can eliminate its market exposure if they can replicate the behaviour of the risk exposure. This is particularly critical to option market makers for eg whose business models entails replicating the risk they are exposed from their customers’ orders. As an example, a bank may sell a put option to a customer. To hedge / replicate the position the bank would need to sell stock and purchase a same strike / expiration call option. This eliminates the bank’s risk. If interested google conversions and reversals.
According to my NTU prof's notes, Replicating Portfolio and Hedging • Portfolio (Phi_t, Psi_t) known as replicating portfolio ... • Above is simple example of hedging strategy Investment strategy that reduces amount of risk carried by issuer of contract Not all hedging strategies are replicating strategies
