Selling a put option is equivalent to buying a call option. Assume that both the options are on the same asset, have the same expiry time and the same strike price.

If I have a long position in a forwards contract, I can decide the quantity of the asset that I want to buy under this contract, depending on the market situation at time T.

Optimal price of a forward contract when dividend is payable during the life of the contract is less than the optimal price of a forward contract under no dividend setup.

A person has short position in a futures contract on one unit of some asset and a short position in a European call option on one unit of the same asset. If the futures price is same as the strike price and the maturity time is the same for both these derivatives, then the payoffs at time T are same for both these derivatives.

Person A and Person B own exact same portfolios. It seems from the current market conditions that their portfolio worth is likely to go down over the period of next three months. Hence, person A hedges her position by entering into some financial contract whereas person B does not carry out any transaction. At the end of the three month period, the portfolio worth for person B can be more than that of person A.

A speculator assess risks involved in each transaction and then enters into a contract which is least risky.

Bid price is generally lower than the offer price.

If the risk free rate of interest in Brazil is more than the risk free rate of interest in India, the optimal futures price for a Brazilian Real is less than its spot price.

For a holder of a European option, payoff at time T (i.e., ignoring payoff at time zero) can never be negative.