Pricing of Discrete Barrier Options with Few Monitoring Points

A barrier option is a financial derivative whose payoff depends on the underlying asset breaching a predefined barrier level. Compared to vanilla options, barrier options are less expensive and may be customized for specific risk management strategies or strategic financial applications. In practice, the underlying asset is monitored only at discrete times, yet accurate and efficient pricing of discrete barrier options remains a challenge. While prior research has primarily focused on near-continuous monitoring, this thesis addresses the pricing of barrier options with only a few monitoring points. Using a Brownian motion-based pricing model, we derive exact pricing formulas for barrier options with up to three monitoring points, and establish a lower bound for the price of any barrier option with at least one monitoring point at maturity. Importantly, we find excellent agreement between our findings and estimates obtained from Monte Carlo simulations. Moreover, we find that the marginal value of additional monitoring points diminishes as their number increases, if they are evenly distributed. Our findings provide further insights into the pricing of discrete barrier options and help bridge the gap to the near-continuous case.

Sv: En barriäroption är ett finansiellt derivat vars avkastning beror på att den underliggande tillgången bryter mot en fördefinierad barriärnivå. Jämfört med vanliga optioner är barriäroptioner billigare och kan anpassas för specifika riskhanteringsstrategier eller strategiska finansiella tillämpningar. I praktiken övervakas den underliggande tillgången endast vid diskreta tidpunkter, men korrekt och effektiv prissättning av diskreta barriäroptioner är fortfarande en utmaning.