MATBUS470 Lecture Notes - Lecture 5: Dividend Yield, Forward Price, Investment

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Asset that pays a known income, where i = present value of the income = c*e^(-rt) Forward price on an asset with a known dividend yield. Let q be the dividend yield q (st* dt) is the amount paid between t & t+dt. If the dividend yield is continuously reinvested back into the asset, then starting with 1 unit at time. 0, an investor will have e^qt units of the asset at time t. Enter a long forward to buy 1 unit of the asset at time t for price f0. Also invest f0 e^(-rt) in the risk free investment. Portfolio 2: buy e^(-qt) units of the asset < - less than 1 unit and continuously reinvest the dividend yield back into the asset. 0 + f0 e^(-rt) (st - f0 ) +f0 = st e^(-qt) s0. Same payo , so under the no arbitrage assumption, the cost must be equal. F0 = e^((r-q)t) s0 = e^(-qt) s0 e^(rt)

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