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Introduction to Financial Markets Unit 7 Derivatives: Options Prof. Dr. M. De Ceuster Prof. Dr. M. De Ceuster Introduction to Financial Markets 1 / 17  Options...

Introduction to Financial Markets Unit 7 Derivatives: Options Prof. Dr. M. De Ceuster Prof. Dr. M. De Ceuster Introduction to Financial Markets 1 / 17  Options Section 1 Options Prof. Dr. M. De Ceuster Introduction to Financial Markets 2 / 17  Options Definition A plain vanilla option is a security that gives the owner at a maturity date (expiration date) (European style) or up to the maturity date (American style) the right to buy (call option) or sell (put option) a fixed amount of an underlying (contract size) at an agreed price (strike price, exercise price). The act of using the right by the option buyer is referred to as exercising the option. Prof. Dr. M. De Ceuster Introduction to Financial Markets 3 / 17  Options Definition On any trading day the owner of the option can Retain the option and do nothing, Sell the option at it’s concurrent market price, Exercise the option if the contract allows it. On the maturity day the option can also expire. Prof. Dr. M. De Ceuster Introduction to Financial Markets 4 / 17  Options Terminology Positions: Long position = option buyer (who holds the right to exercise the option). Short position = option seller or option writer (who holds the contingent obligation). Standard and beyond Plain vanilla options are standard European and American calls and puts. Exotic options deviate in their specification in one way or another from vanilla options. Examples are barrier options, Asian options, lookback options, compound options,... Prof. Dr. M. De Ceuster Introduction to Financial Markets 5 / 17  Options Terminology Options (as such) Embedded options Callable bonds Convertible bonds Mortgages Real options Prof. Dr. M. De Ceuster Introduction to Financial Markets 6 / 17  Options Terminology The option is in-the-money if immediate exercise would lead to a positive cash flow: Call : If S t > K Put : If S t < K The option is out-of-the-money if immediate exercise would lead to a negative cash flow. The OTM option will not be exercised. The option is at-the-money if immediate exercise would lead to a zero cash flow. S In empirical research the ratio K is often used to measure the degree of moneyness. Prof. Dr. M. De Ceuster Introduction to Financial Markets 7 / 17  Options The Quoted Premium The option premium is quoted per unit of the underlying. To obtain the total purchase cost, weneed to multiply the quoted option premium with the contract size and we have to add the transaction costs. The premium is often decomposed in an intrinsic value (i.e. St - K ) and a time value (i.e. premium - intrinsic value). Prof. Dr. M. De Ceuster Introduction to Financial Markets 8 / 17  Options Recall The payoff from a contract is the net cash flow generated by the contract at maturity date. The payoff is the value of a contract at the maturity date. Prof. Dr. M. De Ceuster Introduction to Financial Markets 9 / 17  Options The Payoff of the Option Contract Variable Notation Strike Price K Maturity date T Spot price S Value of the call at date T fTposition Value of the put at date T fTposition Payoff fTlong call = max(S T ≠ K , 0) f long put = max(K ≠ S T , 0) T Recall : fTshort = ≠f Tlong Prof. Dr. M. De Ceuster Introduction to Financial Markets 10 / 17  Options Payoff Diagrams of Options Long Call Long Put 25 25 20 20 15 15 PayOff PayOff 10 10 5 5 0 0 0 10 20 30 40 50 0 10 20 30 40 50 S S Short Call Short Put 0 0 − − 5 5 −1 −1 0 0 PayOff PayOff −1 −1 5 5 −2 −2 0 0 −2 −2 5 5 0 10 20 30 40 50 0 10 20 30 40 50 S S Prof. Dr. M. De Ceuster Introduction to Financial Markets 11 / 17  Options The Profit Diagram Since an option premium has to be paid, a lot of traders ‘add’ the premium to the payoff profile to obtain a profit diagram. ProfitTlong = fTlong —premium Profitshort = f short + premium T T In doing so, most of the time, the time value of money is neglected. The payoff is realised at the maturity date, the premium is paid upfront. In order to correct for this some people will adjust the payoff with the premium compounded to the maturity date. Prof. Dr. M. De Ceuster Introduction to Financial Markets 12 / 17  Options Breaking Even (Ignoring Time Value of Money) The option holder will break even i.e. will realize a zero profit if the long regains his paid premium, the short loses his received premium. Prof. Dr. M. De Ceuster Introduction to Financial Markets 13 / 17  Options The Profit diagram of the Long Call Long Call 15 Payoff Profit 10 5 Profi t 0 − 5 0 10 20 30 40 50 S Prof. Dr. M. De Ceuster Introduction to Financial Markets 14 / 17