Explain how the Black–Scholes–Merton call formula can be read as a leveraged holding of the underlying
The idea
BSM reads as a replicating portfolio. A call equals a long position in N(d1) units of the underlying, scaled down by the dividend discount factor, financed partly by borrowing the present value of the strike times N(d2). In symbols, where nS is the call's delta, B the present value of the strike and nB its weight N(d2), the risk-neutral chance of exercise, the call is c = nS × S − nB × B. The call is a leveraged long position, rebalanced as the price moves. A put is the mirror image: short the underlying and lend. For a currency option, the foreign risk-free rate plays the role of δ. The trap is taking the borrowing to be the full present value of the strike instead of weighting it by N(d2).
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