We construct a discrete time self-financing portfolio comprised of call options short and stock shares long which is riskless and grows at a fixed rate of return. It is also shown that when shorting periods tend to zero then so devised portfolio turns into the Black-Scholes bond replication. Unlike in standard approach the analysis presented here requires neither Ito Calculus nor solving the Heat Equation for option pricing.
A Discrete Time Counterpart of the Black-Scholes Bond Replication Portfolio,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 1,
1, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol1/iss1/3