Consider a financial instrument replicated by one long stock and two call options(one long and one short) with different strikes prices. How would the price of the instrument change if it was announced that it would pay a (non-zero) dividend in half a year? Assumption: the current stock price is assumed not to change due to the dividend announcement.

Donâ€™t worry, i answered my own question. For those interested:

The instrument is replicated using one long and one short call option and a stock; therefore the value of the call options and the stock is deterministic of the value of the instrument. Dividends have the effect of reducing the stock price on the ex-dividend date, which in turn negatively effects call options. Options exercised at maturity can be analysed by assuming the stock price is the sum of a riskless component-the known dividends during the life of the option- and a risky component S(0). This is because when the option matures, the dividends will have been paid and the riskless component will no longer exist. The riskless component at any given time, is the present value of all dividends during the life of the option. Black Scholes assumptions can be utilised provided the stock price is reduced by this riskless component. As a result, the value of the call options in the replicating portfolio will be reduced, while the stock price will also be reduced by an amount equal to the dividend. Note that the delta ratio compares the change in the price of the underlying asset to the corresponding change in the price of a derivative; a higher delta translates to a greater change in price. (I failed to mention the short call option has a higher delta than the long option) The short call option has a higher delta compared to the long call option, which has the net effect of reducing the value of the call option portfolio. Combined with a reduced stock price, the price of the instrument will decrease.