Consider an option trader with a portfolio of options. Two of the positions are written against the same stock (Risky Ltd). The option trader seeks to delta hedge her exposure dynamically over the next two weeks. Once initiated, the hedged position will be held to the end week 1. At this point it will be rebalanced and the revised hedge position held until the end of week 2. At this point the hedge will be closed out. The following option positions (written against Risky Ltd) are held: Position 1: European call, Strike $25, maturity 1 month, Short 40 options Position 2: European put, Strike $27, maturity 3 weeks, Long 50 options

Risky Ltd stock price is currently trading at $26. Its expected volatility is 35% p.a. The risk-free rate is 3% p.a continuously compounded. You may assume the BSM assumptions hold true. a) How many units of the stock should the option trader buy or sell to delta hedge the exposure on initiation of the hedge. Show all workings