Article Contents
Article Contents

# Pricing bond options in emerging markets: A case study

• We propose two methodologies to price sovereign bond options in emerging markets. The motivation is to provide hedging protection against price fluctuations, departing from the not liquid data provided by the stock exchange. Taking this into account, we first compute prices provided by the Jamshidian formula, when modeling the interest rate through Vasicek model, with parameters estimated with the help of the Kalman filter. The second methodology is the pricing strategy provided by the Black-Derman-Toy tree model. A numerical comparison is carried out. The first equilibrium approach provides parsimonious modeling, is less sensitive to daily changes and more robust, while the second non-arbitrage approach provides more fluctuating but also what can be considered more accurate option prices.

Mathematics Subject Classification: Primary: 91B25; Secondary: 62M05.

 Citation:

• Figure 1.  Monthly returns of AFAPS. Year 2013 (in UYU).

Figure 2.  Example of a four period binomial tree.

Table 1.  Option prices for zero coupon USD (left) and UI bonds (right). VK and BDT stand for Vasicek and Black-Derman-Toy models respectively

 USD 3 months option prices UI 3 months option prices Strike CALL PUT Strike CALL PUT VK BDT VK BDT VK BDT VK BDT $99.50$ $0.000$ $0.000$ $5.268$ $5.069$ $94.00$ $0.000$ $0.000$ $3.617$ $3.580$ $97.06$ $0.000$ $0.000$ $2.831$ $2.641$ $92.18$ $0.000$ $0.000$ $1.817$ $1.782$ $94.69$ $0.001$ $0.187$ $0.464$ $0.459$ $90.40$ $0.117$ $0.240$ $0.173$ $0.259$ $92.37$ $1.853$ $2.044$ $0.000$ $0.007$ $88.65$ $1.675$ $1.711$ $0.000$ $0.001$ $90.11$ $4.111$ $4.291$ $0.000$ $0.000$ $86.93$ $3.377$ $3.405$ $0.000$ $0.000$ USD 6 months option prices UI 6 months option prices Strike CALL PUT Strike CALL PUT VK BDT VK BDT VK BDT VK BDT $99.55$ $0.000$ $0.000$ $5.117$ $4.852$ $94.76$ $0.000$ $0.000$ $3.341$ $3.128$ $97.36$ $0.000$ $0.000$ $2.934$ $2.673$ $93.15$ $0.000$ $0.002$ $1.766$ $1.569$ $95.22$ $0.015$ $0.160$ $0.801$ $0.703$ $91.58$ $0.086$ $0.267$ $0.316$ $0.300$ $93.12$ $1.129$ $1.599$ $0.000$ $0.058$ $90.03$ $1.286$ $1.484$ $0.001$ $0.008$ $91.07$ $3.336$ $3.582$ $0.000$ $0.003$ $88.51$ $2.773$ $2.958$ $0.000$ $0.000$ USD 1 year option prices UI 1 year option prices Strike CALL PUT Strike CALL PUT VK BDT VK BDT VK BDT VK BDT $99.65$ $0.000$ $0.000$ $4.561$ $4.224$ $96.25$ $0.000$ $0.000$ $2.673$ $2.229$ $97.94$ $0.000$ $0.000$ $2.867$ $2.538$ $95.10$ $0.000$ $0.005$ $1.573$ $1.136$ $96.26$ $0.000$ $0.069$ $1.204$ $0.950$ $93.95$ $0.037$ $0.231$ $0.511$ $0.277$ $94.61$ $0.441$ $0.918$ $0.011$ $0.170$ $92.83$ $0.619$ $1.047$ $0.002$ $0.021$ $92.99$ $2.034$ $2.373$ $0.000$ $0.023$ $91.71$ $1.669$ $2.086$ $0.000$ $0.001$
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