7.0 Conventions and notation

• $t$ is time in years. Calendar day counts use ACT/365, so 54 days is $T=54/365$.
• $S_t$ is the spot price of the underlying, $F_t$ (or $F_{t,T}$) the futures price for delivery at $T$, $G_t$ the forward price when the distinction matters (7.2), $K$ the delivery price written into a forward contract.
• $r$ is the continuously compounded risk-free rate for the relevant maturity. A rupee invested at time 0 is worth $e^{rT}$ at $T$. When rates vary over time, $B_t=\exp\left(\int_0^t r_s\,ds\right)$ is the value of the money-market account and $D_t = 1/B_t$ is the discount factor.
• $q$ is a continuous dividend yield: holding one unit of an index for $dt$ pays $qS_t\,dt$ in dividends.
• $\tau = T-t$ is the time to delivery.
• Basis is $b_t = F_t - S_t$ in this course. Hull defines basis as $S_t - F_t$. Every formula below uses $F - S$; translate with care when reading Hull.
• "Lot" means the contract multiplier: the number of units of the underlying per contract. A Nifty future with lot 65 at price 24,719.10 has notional value $65 \times 24{,}719.10 = \text{₹}16{,}06{,}741.50$.

A derivative in this module means a contract whose payoff is a function of another asset's price (the underlying). Rupee amounts use the Indian digit grouping: ₹1 lakh = ₹1,00,000 and ₹1 crore = ₹1,00,00,000.