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CONVERTIBLE SECURITIES AND DERIVATIVES (Types of Warrant (Equity warrants…

- - - - F = S x e^(r x t)
        Where:
        F = the contract's forward price
        S = the underlying asset's current spot price
        e = the mathematical irrational constant approximated by 2.7183
        r = the risk-free rate that applies to the life of the forward contract
        t = the delivery date in years
        
        For example, assume a security is currently trading at $100 per unit. An investor wants to enter into a forward contract that expires in one year. The current annual risk-free interest rate is 6%. Using the above formula, the forward price is calculated as:
        F = $100 x e ^ (0.06 x 1) = $106.18
  - - - F0 = S0(1 + rf – d)
        F0 = Initial Futures Price
        S0 = Initial Stock Price
        rf = Risk-Free Interest Rate
        d = Dividend Yield
        
        For example, industrial metals, precious metals, oil, natural gas and other energy products, oils, seeds, grains, livestock and even carbon credits all have tradable futures contracts available.
  - - - Options Pricing
        
        Intrinsic Value (Call) = Underlying Price – Strike Price
        Intrinsic Value (Put) = Strike Price – Underlying Price
        In-the-Money (Call) = Strike Price < Underlying Price
        In-the-Money (Put) = Strike Price > Underlying Price
        Time Value = Premium – Intrinsic Value
        Option Premium = Intrinsic Value + Time Value
  - - - Swaps can reduce each party’s financial risk
        
        For example, on Dec. 31, 2006, Company A and Company B enter into a five-year swap with the following terms:
        Company A pays Company B an amount equal to 6% per annum on a notional principal of $20 million.
        Company B pays Company A an amount equal to one-year LIBOR + 1% per annum on a notional principal of $20 million.
        LIBOR, or London Interbank Offer Rate, is the interest rate offered by London banks on deposits made by other banks in the eurodollar markets. The market for interest rate swaps frequently (but not always) uses LIBOR as the base for the floating rate. For simplicity, let's assume the two parties exchange payments annually on December 31, beginning in 2007 and concluding in 2011.
        At the end of 2007, Company A will pay Company B $20,000,000 6% = $1,200,000. On Dec. 31, 2006, one-year LIBOR was 5.33%; therefore, Company B will pay Company A $20,000,000 (5.33% + 1%) = $1,266,000. In a plain vanilla interest rate swap, the floating rate is usually determined at the beginning of the settlement period. Normally, swap contracts allow for payments to be netted against each other to avoid unnecessary payments. Here, Company B pays $66,000, and Company A pays nothing. At no point does the principal change hands, which is why it is referred to as a "notional" amount.
- - - - C = S N(d1) - X e-rT N(d2)
        Where,
        C = price of the call option
        S = price of the underlying stock
        X = option exercise price
        r = risk-free rate
        T = time until expiration
        N() = area under the normal curve
        d1 = [ ln(S/X) + (r + σ2/2) T ] / σ T1/2
        d2 = d1 - σ T1/2
        
        This formula is for European-style options and, though American-style options
        
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