 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Mathematics course of the University of Oxford

Year 3 of the mathematics course of the University of Oxford

Mathematical models of financial derivatives course of the University of Oxford

Past exam of the mathematical models of financial derivatives course of the University of Oxford

2015

{c}

A <replicating strategy> holds $\Delta$ shares and a current cash amount $b$ in the <bank account>. Matching the two next values gives
$$
\Delta S^u_{t+1}+Rb=V^u_{t+1},\qquad
\Delta S^d_{t+1}+Rb=V^d_{t+1}.
$$
Solving this <linear system>,
$$
\Delta=\frac{V^u_{t+1}-V^d_{t+1}}{S^u_{t+1}-S^d_{t+1}},\qquad
b=\frac{S^u_{t+1}V^d_{t+1}-S^d_{t+1}V^u_{t+1}}{R(S^u_{t+1}-S^d_{t+1})}.
$$
By <no-arbitrage>, the claim costs $V_t=\Delta S_t+b$. Collecting the coefficients of its two future values yields
$$
\boxed{V_t=R^{-1}\bigl[qV^u_{t+1}+(1-q)V^d_{t+1}\bigr],\qquad
q=\frac{RS_t-S^d_{t+1}}{S^u_{t+1}-S^d_{t+1}}.}
$$
The physical <probability> $p$ does not appear: replication fixes the price of this <contingent claim> from traded prices.

Solution

Past exam of the mathematical models of financial derivatives course of the University of Oxford / 2015 / 1 / b / Solution

Past exam of the mathematical models of financial derivatives course of the University of Oxford / 2015 / 1 / b / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematical models of financial derivatives course of the University of Oxford / 2015 / 1 / b / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)