Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries
Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries
Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries
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Percentage change <strong>in</strong> price due to duration = -4.0555 x (+0.01) x 100= -4.0555%Percentage change <strong>in</strong> price due to convexity = l/2x20.I886x(+O.OI)(+O.OI)x 100= 0.1009%Total percentage change <strong>in</strong> price = -4.0555% + 0.1009%= -3.9546%When rate <strong>in</strong>creases, the convexity actually decelerates the pricedepreciation. As shown on the graph on page 44, the tangent l<strong>in</strong>e liesbelow the theoretical price l<strong>in</strong>e.underestimates the true security price.This implies that duration alwaysAll we are do<strong>in</strong>g here is to figure out what the true theoretical prices are.In reality, observed market prices may be different from the theoreticalprices because of bid-ask spread, demand and supply, market liquidity,market sentiment, etc. Asset pric<strong>in</strong>g is more an art than an exact scienceand all mathematical models are just tools to facilitate the pric<strong>in</strong>g analysis.I had once tried to confirm the market value of a multi-billion dollar, illiquidand below-<strong>in</strong>vestment-grade bond (or junk bond) portfolio <strong>in</strong> order todeterm<strong>in</strong>e the viability of the <strong>in</strong>stitution who held these bonds. A worldfamousjunk bond consultant group was called <strong>in</strong> to do the evaluation. Afterdays of hard work, the consultants delivered their f<strong>in</strong>al analysis. The marketvalues of most of these bonds given <strong>by</strong> the consultants ranged between 55and 85 percent of par. The consultants said that if everyth<strong>in</strong>g (<strong>in</strong>clud<strong>in</strong>g theeconomy, market sentiment of the company, market sentiment of junkbonds, <strong>in</strong>terest rates, management's ability, etc.) went well, the price couldbe 85, and if everyth<strong>in</strong>g did not go well, the price could be 55. In otherwords, the user of the analysis had to make a lot of subjective assumptions<strong>in</strong> order to come to a def<strong>in</strong>itive conclusion.tDuration and convexity are very useful <strong>in</strong> bond pric<strong>in</strong>g analysis. They arealso useful tools <strong>in</strong> trad<strong>in</strong>g and derivatives activities. Traders often usesometh<strong>in</strong>g called price value basis po<strong>in</strong>t (PVBP) to measure the sensitivityof risk of their positions. PVBP uses the duration concept to measure theDuration and Convexity