TY - JOUR T1 - It Is Time to Shift Log-Normal JF - The Journal of Fixed Income SP - 37 LP - 51 DO - 10.3905/jfi.2017.27.2.037 VL - 27 IS - 2 AU - Ren-Raw Chen AU - Pei-Lin Hsieh AU - Jeffrey Huang Y1 - 2017/09/30 UR - https://pm-research.com/content/27/2/37.abstract N2 - The contribution of the LIBOR Market Model (LLM) by Brace, Gatarek, Musiela [1997] and Miltersen, Sandmann, and Sondermann [1997] is its justification of using the BS model in the cap market. This convenience has helped the industry incredibly in that a simple solution is enough to price caps (and floors). Yet this convenience comes with a price, which is that its drift adjustment under the forward measure is unconstructive. Furthermore, assuming LIBOR to be log-normal surrenders the flexibility that recent LIBOR is normally distributed. In this paper, we provide an alternative to reformulate the LLM so that both concerns are addressed easily. Not only can LIBOR distribution switch between normal and log-normal, but also the drift adjustment is no longer stochastic and instead easy to implement. We also show how to translate the “Black vol” (the volatility implied by the Black model) and the “bp vol” (known as the basis point volatility). Empirically we have observed that when rates are low, the basis point volatility is more stable (i.e., they follow the normal distribution more closely) and when they are high the Black volatility is more stable (i.e., they follow the log-normal distribution more closely).We derive also specifically how the cap volatility curve (Tj × Tj+1 only) is related to the swaption volatility surface(Ti × Tj). We also comment on the swap measure.TOPICS: Fixed income and structured finance, fixed-income portfolio management, portfolio theory ER -