If you're thinking: this is fascinating, what other schedules can we use, besides exponentially increasing or decreasing the coupon over time? Assume we have a

If you're thinking: this is fascinating, what other schedules can we use, besides exponentially increasing or decreasing the coupon over time? Assume we have a market with n different perpetuities: p1,p2...,pn. When we shift the coupon schedule of any of these securities in time, we would like the resulting security to be expressible as a linear combination of the n perpetuities. p1...p2 should be the basis of a vector space of coupon schedules which is stable for time shifts. As it turns out, any vector space with such a property will be the sum of spaces spanned by { exp(lambda t) t^k | k < K } or { exp(lambda t) t^k cos t, exp(lambda t) t^k sin t | k < K } for lambda real. So for instance, we could have the following set of coupon schedule, and it would be stable: {1, exp(-0.03 t)} But so would: {1, t, exp(-0.03 t)} or even {1, cos t exp(-0.05 t), sin t exp(-0.05 t)} etc.