Forward & Future Contract pricing

Short overpriced, long underpricedFP is the fwd price agreed to at the initiation t=0 of the contract, not the current mkt forward price(FP = fwd price at no arbi)mkt spot increase, fwd price increase after T=0-> long wins Vtlong = positive, Vtshort = negativemkt spot and fwd prices decrease, Vt short is positive A stock, a stock portfolio, or an equity index may have expected dividend payments over the life of the contract. So we have to adjusted spot for present value of div pay or fwd price for future div pay in the formula. The no-arbitrage price of an equity forward contract is Formula adjusted for present value of remaining expected discrete dividends at time t (PVDt) to get:

To calculate equity forward contracts with continuous dividends (not discrete) at div yield rate on the index continuous time case -> value of forward contract is Forward price for a coupon paying bond (use for div paying stock portfolio):PVC = (1000 x c.p rate)/ 1+rft/365value of fwd contract before expiration :FRA (Forward rate agreement) Long position borrow money- (long the loan with the contract price being the interest rate on the loan at LIBOR) but if LIBOR is higher than specified in the FRA so this position has right to borrow below mkt rates and long will receive payment .If LIBOR is less than FRA -> short receive cash payment (short has the right to lend above mkt rate -> positive value)Continuous time price and value for curr fwd contractVt in both case is the value in domestic currency units for a contract covering one unit of the Fcurr,For the settlement pmt in home curr on a contract, simply multiply this amount by the notional amount of Fcurr coverd in the contract.Hedge RatioHedge ratio = Portfolio value($P) /Nominal value of 1 contract Nominal value of 1 contract =contract multiplier x S0 S0 = index value F0 = Future priceCross Hedging Return on Hedged Position = $Prp - HNrfReturn hedged variance = P22 + (HN)2 - 2PHN x covariance(rp, rs&p)P = $ value of your port = variance of port H = # of contract use to hedgeN = nominal value of each contract($)= variance of index (S&P in this case)To minimize variance w.r.t. H (to minimize risk), differentiate and set equal to zero:

Basis Risk (aka residue risk) bcz you cant hedge everything so there is some left over risk

() Var(r)=systematic risk + Non-systematic (or residual risk)Future contract Correlation between the underlying asset value and interest rates is Positive. Investors will prefer to go long in future, future price > forward priceZero Future price = Forward priceNegative Investors prefer long in forward contract So Forward price > Future price Cash and Carry Arbitrage (If contract is overpriced/Reversed C&CA if contract is underpriced) Step at initiation of contract:1)Borrow money for the term of the contract at market interest rates. / lend short sale proceed2)Buy the underlying asset at the spot price./ short sale3)Sell (go short) a futures contract at the current futures price. /longStep at contract expiration:1) Deliver the asset and receive the futures contract price.(receive the asset and pay futures price then return the asset to cover short sale) 2) Repay the loan plus interest at mkt int(collect loan proceeds) (The table compare T=0 to T= expiration)Monetary and Non monetary benefits and costs associated with holding the underlying assetCommodity -> storage cost increase futures priceFinancial asset -> earn div,interest, c.p. pmt -> decrease no arbi futures price no storage cost