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# LectSlide1 - EC3070 FINANCIAL DERIVATIVES FUTURES MARKING...

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EC3070 FINANCIAL DERIVATIVES FUTURES: MARKING TO MARKET The holder of a futures contract will be required to deposit with the brokers a sum of money described as the margin, which will be calculated at a percentage of the current spot price S 0 of the asset. At the end of each day of trading, the margin will be adjusted to reﬂect the gains or losses of the contract holder. Should the cumulated losses reduce the margin to below a certain thresh- old level, described as the maintenance margin, then extra funds will be called for to maintain its level. The process of adjusting the margin account is described as marking to market. Its effect is to ensure that, at the end of any day of futures trading, when the daily settlements have been made, there will be no outstanding obligations. This will allow the position of the contract holder to be closed without further losses or gains, thereby virtually eliminating the risk of a default on the contract. 1

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EC3070 FINANCIAL DERIVATIVES Let F τ | t be the value at time t of a futures contract that is to be settled at time τ , and let δ t be the gains or loses realised on day t , which is a sum that must be paid to the brokers or paid by them to the contract holder. Day Futures Price Gain or Loss t F τ | t δ t 0 F τ | 0 1 F τ | 1 δ 1 = F τ | 1 F τ | 0 2 F τ | 2 δ 2 = F τ | 2 F τ | 1 . . . . . . . . . τ F τ | τ = S τ δ τ = S τ F τ | τ −| 1 It can be assumed that F τ | t S τ as t τ , which is to say that the futures price converges to the spot price as the delivery time approaches. 2
EC3070 FINANCIAL DERIVATIVES The settlement on the final day, which is δ τ = S τ F τ | τ 1 , will be a negligable amount. At that time, the cumulated total of the adjustments is τ t =1 δ t = S τ F τ | 0 ,

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