No-arbitrage condition for curves

almostcutmyhair · June 24th, 2014, 3:45 pm

I have three questions. What are the mathematical conditions (or constraint) for the the following to be arbitrage-free:1) Yield curves2) Commodity forward curves (seasonal and non-seasonal)3) Credit curves

pcaspers · June 24th, 2014, 5:23 pm

1) / 3) today's discount factors / survival probabilities are decreasing in maturity <=> instantaneous forward / hazard rates are positive at all times

almostcutmyhair · June 24th, 2014, 5:32 pm

QuoteOriginally posted by: pcaspers1) / 3) today's discount factors / survival probabilities are decreasing in maturity <=> instantaneous forward / hazard rates are positive at all timesSo, a convex discount factor/survival prob curve?

pcaspers · June 24th, 2014, 5:37 pm

QuoteOriginally posted by: almostcutmyhairQuoteOriginally posted by: pcaspers1) / 3) today's discount factors / survival probabilities are decreasing in maturity <=> instantaneous forward / hazard rates are positive at all timesSo, a convex discount factor/survival prob curve?no, just decreasing

almostcutmyhair · June 24th, 2014, 6:17 pm

QuoteOriginally posted by: pcaspersQuoteOriginally posted by: almostcutmyhairQuoteOriginally posted by: pcaspers1) / 3) today's discount factors / survival probabilities are decreasing in maturity <=> instantaneous forward / hazard rates are positive at all timesSo, a convex discount factor/survival prob curve?no, just decreasingAlright...I see.So that guarantees no-arbitrage w/o any additional conditions (except positivity)?

BramJ · June 24th, 2014, 6:38 pm

For 2) google for supercontango

pcaspers · June 25th, 2014, 3:02 pm

QuoteSo that guarantees no-arbitrage w/o any additional conditions (except positivity)?yes (if the quantities are inside [0,1] in addition to monotonicity)