Tick all statements which are correct, but do not tick those that are incorrect.a$.$ If there is arbitrage, then a risk$-$neutral distribution exists.b$.$ An American put option should always be exercised before its expiry time.c$.$ The price of a put option and of a call option with the same expiration time and strike price can never be the same.d$.$ A forward contract gives you the right but not the obligation to buy a certain product at a specified time in the future for a fixed price.e$.$ If there is a sporting event with $3$ different outcomes with corresponding odds equal to $\backslash ($ o$\_\{1\}=2,$ o$\_\{2\}=2\backslash ),$ and $\backslash ($ o$\_\{3\}=3\backslash ),$ then there is an arbitrage opportunity for a suitable betting strategy.