Pricing Issues, Hedging and Other Risk Management Tools : Pricing Issues, Hedging and Other Risk Management Tools Rahul Singh, Ph.D.


Cost of Carry Model : Cost of Carry Model It assumes that the market is perfect and there is no commission, no transaction cost, no taxes or bid and ask spread. It helps in determining the spot and futures prices And also the between prices of contracts of different expiry months According to the Cost of Carry theory, futures prices depend on Spot price Cost of warehousing Cost of insurance, if any Cost of financing, if any etc. F = S + C Where F is futures price, S is Spot price, and C is cost of carry.


Slide3: If F > S + C, there is an arbitrage opportunity, cash and carry arbitrage In this, Ar borrows to buy Spot asset, sells futures and carries assets till maturity


Fair Value Commodity Derivatives: Fair Value Commodity Derivatives F = S (1 + r)n F = S (1 + r/m)nm F is futures price, S is spot price, r is cost of financing, n is time of contract in years and m is no. of times compounding in an year At the daily compounding, fair value will be F = Sern Where e = 2.718


Example : Example Cost of 10 gms gold in the spot market is 9000 & the cost of financing is 16% p.a., find out the fair value of 6 months contract by Cost of Carry method. Cost of 10 gms gold in the spot market is 9000 & the cost of financing is 16% p.a., find out the fair value of 6 months contract. Cost of 10 gms gold in the spot market is 9000 & the cost of financing is 16% p.a., find out the fair value of 6 months contract, with continuous compounding.


Arbitraging Example : Arbitraging Example Say price of a product is 280. the forward price for this is 300 for 6 months maturity, and annual interest rate is 10%. theoretical price; F = S + C = 280 + 14 = 294 Since F > S+C, borrow to buy asset and sell on forward as it is overpriced Transaction Today: Sell one forward No cash flow Buy one product -280 Borrow (for 6 months at 10%) 280


Slide7: At Delivery Time: Ft=St=270 Ft=St=300 Ft=St=330 Deliver 1 product 300 300 300 Payback loan with Int. 294 294 294 Differences +6 +6 +6 Thus regardless of the delivery day price, the arbitrage profit is 6 per product. So, note that profit is independent of final spot pricing,


The Pricing Behaviour: Basis : The Pricing Behaviour: Basis Basis is difference between cash and futures price If cash price > futures, basis is positive; it is negative in otherwise case Basis is negative in normal market, and positive in Inverted Market (this happens for a fair demand and supply economics; the invert situations do take place in reverse demand and supply economics) If cash price increases at faster rate than the rate of futures price, basis is said to be strengthening A strong basis indicates a high demand or short supply in the market. i.e.; at the time of maturity, basis should be Zero, spot price of the day and futures price must be same; if not, there is an arbitrage opportunity. The process of moving towards zero is called convergence.


Exercise: Convergence of Prices : Exercise: Convergence of Prices Can you draw different convergence of the prices in a bull and bear market indicating the basis for positive and negative.


Example: Arbitrage against Convergence : Example: Arbitrage against Convergence Suppose that an instant before the closing, trading ceases on the delivery date. The spot price of the product is 290. the futures price of the expiring contract is 289. What/how shall be the arbitrage opportunity and the benefit economics?


Pricing Variables: Spread : Pricing Variables: Spread It is spread in two futures prices A normal market would indicate a lower price of near month than the far month futures price, else an inverted market. Intra commodity spread is know as difference of price in two futures contract of same commodity having different expiry months Inter commodity spread is difference of two commodity having same expiry month Spread is used to assess the pricing behaviour of the products at different stages and thus it is calculated on continuous basis.


Risk Management in Futures: Risk Management in Futures Hedging is the offsetting of positions in the spot and futures market. Long (anticipatory) and short hedge have buying and selling of futures contracts respectively. Most hedges happens to be Cross Hedge, means assets are not same. Hedge ratio is defined to be the ratio between the number of futures contracts required to hedge one unit of a cash asset that must be hedged.


Slide13: HR = ρ {σ (∆CP)/ σ (∆FP)} Where ρ is coefficient of correlation between ∆ cash and ∆ futures prices. In January, A buys 10 gm gold from cash market. He decides to hedge for any risk, and sells futures. The σ for cash and futures is 1.3 and .9 respectively. ρ for 30 days is 0.75 for a standard contract of 1 kg. Find Hedge Ratio and give interpretation.


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