[pt] Este trabalho tem como objetivo testar se cone de volatilidade aplicado ao mercado de opções brasileiro pode trazer informações adicionais à decisão de compra e venda de volatilidade. Outra contribuição deste trabalho é mostrar se os efeitos do sorriso de volatilidade e da estrutura a termo da volatilidade persistem diante de operações realizadas com o cone de volatilidade.Os resultados indicam que a comparação da volatilidade implícita com o cone de volatilidade pode ser um indicador eficiente para prever a evolução da volatilidade futura. Além disso, não só foi evidenciada a eficiência do cone como há indícios de que os ganhos são ainda mais acentuados para operações com opções dentro-do-dinheiro. Quanto a operações com opções de curto e médio prazo de duração até o exercício não existe índicos suficientes que comprovem a diferença nos resultados obtidos com a utilização do cone de volatilidade. / [en] The present study has the objective of testing if the volatility cone applied to the option market can improve the decision process of buy and sell volatility. Another contribution from this study is to assess if the volatility smile and the term structure of volatility persist when the volatility cone is used to build some operation.The results indicate that the balance of implied volatility and the volatility cone can be an efficient indicator to forecast the tendency of future volatility. Moreover, there are some indications that in-the-money options yield better results than others. On the contrary, there is no indication that short-term and medium-term options yield different results when using the volatility cone.

A large part of the foreign exchange market concerns the trading of FX swaps. While entering a position in a FX swap does not cost any money, banks earn money on FX swaps when their customers cross the bid/ask spread, creating a perceived transaction costs for the swaps. To hedge the risks of their customer positions, banks enter new positions in FX swaps with other banks, crossing the same bid/ask spread. Traditional hedging methods does not take perceived transaction costs into account when determining hedge positions, resulting in greater portfolio losses than necessary for the banks. Therefore, the topic of hedging while taking transaction costs into account could be of great value. When valuing FX swaps and estimating risk factors in a FX environment, term structures need to be estimated for pricing the instruments. The estimation of term structures can be done using several ap- proaches, among them bootstrapping and interpolating the curve or parameterizing the curve, assuming it to be described by a functional form. These traditional methods of term structure measurement has the downside of being unstable and fluctuating greatly over time because of different local optimas each day, or result in very large pricing errors due to certain instruments needing to be excluded from the term structure measurement. These attributes result in capturing extra, unnecessary volatility in the curves which does not model the true risk, consequently estimating the risk factors wrongly when risk management and hedging needs to be done. The estimation of good quality term structures which are stable over time and result in low pricing errors are therefore of great interest to study. In this thesis, a FX swap portfolio is hedged using a Stochastic Programming (SP) model developed by Blomvall and Hagenbj ̈ork (2020). For the valuation of FX swaps in the portfolio and the generation of risk factors for the model, term structures were estimated using a multiple yield curve framework of Blomvall and Ndengo (2013), which penalizes pricing errors and use regularization functions to produce smooth curves. For both the term structure measurement method and the hedging method, a critical part affecting the per- formance of the methods lies in choosing good parameter values, which is what has been the main purpose of this study. The results show that good quality term structures can be estimated using the multiple yield curve frame- work if good parameter choices are made. The resulting curves fulfill the criteria of being stable over time while also keeping the price errors out-of-sample small. A portfolio hedged using a SP-model with certain chosen parameter values and also using the good quality term structures estimated is shown to eliminate a great deal of risk compared to an unhedged portfolio. When compared with a traditional hedging model called the Boxes model, the SP-model gains value from taking perceived transaction costs into account and thus manages to hedge the risks less costly than the Boxes model does.

Masters of Commerce / This paper uses 3 - month and 12 - month market Negotiable Certificates of ( I . Deposit (NCO) rates to test whether greater transparency by the South African Reserve Bank has reduced expectational errors in the money markets. It does so by comparing the relative differences (between the implied forward rates-as indicators of expected future spot rates-and the actual 'future'spot rates) between the period before greater transparency and the period after greater transparency. Empirical evidence for the sample period indicates that greater ransparency by the South African Reserve Bank co-incided with reduced expectational errors in the money markets. Thus, the implied forward rates after greater transparency may well have been better predictors of future spot rates than before greater transparency, although causality has not been proved.

In this dissertation, we investigate the spread option pricing problem with stochastic interest rate. First, we will review the basic concept and theories of stochastic calculus, give an introduction of spread options and provide some examples of spread options in different markets. We will also review the market efficiency theory, arbitrage and assumptions that are commonly used in mathematical finance. In Chapter 3, we will review existing spread pricing models and term-structure models such as Vasicek Mode, and the Heath-Jarrow-Morton framework. In Chapter 4, we will use the martingale approach to derive a partial differential equation for the price of the spread option with stochastic interest rate. In Chapter 5, we will study the spread option numerically. We will conclude this dissertation with ideas for future research.

Over recent years, the economic climate on the Swedish office market has been advantageous, and, as a result, both property prices and market rents have been on a constant rise for almost a decade. Moreover, an increased demand for flexibility in lease terms has been seen on the market, which begs the question; how would changing preferences in length of tenure affect rent levels? There exist several convincing theoretical cases that leases should yield different pricing dependent on its maturity and expectation about future market conditions. The conceptual framework developed by Grenadier (1995, 2005) has been used for the valuation of general leasing contracts and lease terms - applying an option-pricing approach. In total, three papers have analysed the effect length of tenure has on office equilibrium lease rates. However, the empirical evidence, to this date, has been inconclusive in its result when trying to isolate the effects. The purpose of this report is to investigate the relationship between rent and lease maturity. A hedonic pricing model will be developed, which allows for different shapes of the term structure curve, building on the model created by Gunnelin and Soderberg (2003), while controlling for price-relevant characteristics omitted in previous research – such as, building quality, quality of office premise, location, and tenant industry. The model will be used in an empirical study applied to commercial office contracts in Stockholm, Sweden, concluded between 2012 and 2019. The data used in the regression comprise of 1 508 office leases, contracted on the Stockholm market during the investigated period. The result showed a significant term structure for 4 out of 8 years for the full sample, and 5 out of 8 years for the subsample only including leases signed in the CBD. Concludingly, giving further evidence to the reasoning that the market adjusts the rents after lease length, according to future market expectations.

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[pt] A relação entre preços de ativos, expectativa de política monetária, e liberação de dados macroeconômicos tem sido avaliada pela literatura há bastante tempo. Essa dissertação estuda as implicações da ancoragem das expectativas de longo prazo de inflação, como instrumento de política monetária, para a estrutura a termo das taxas de juros. Particularmente, este trabalho objetiva entender como esse mecanismo se conecta ao padrão de variabilidade temporal de ambas a volatilidade dos retornos nominais e a sensibilidade dos mesmos a novidades macroeconômicas. Tendo isso em vista, um modelo Novo-Keynesiano com duas principais características é apresentado. Primeiro, os agentes possuem crenças subjetivas ao invés de expectativas racionais. Eles aprendem sobre o target de inflação definido pelo banco central e suas expectativas podem se tornar ancoradas ou desancoradas, dado o estado da economia. Segundo, a aversão ao risco dos consumidores varia ao longo do tempo. O modelo possui uma principal predição: a sensibilidade da estrutura a termo da taxa de juros com relação a supresas de inflação não apenas varia no tempo, mas depende do estado da economia. / [en] The relation between asset prices, monetary policy expectations, and macroeconomic data releases has long been assessed by the literature. This dissertation addresses the implications of the anchoring or unanchoring of long-run inflation expectations, as a stance of monetary policy, to the term structure of bond yields. In particular, it aims to understand how this mechanism is connected to the time-varying pattern of both the volatility of nominal yields and their sensitivity to macroeconomic surprises. To that matter, we present a New-Keynesian model with two main characteristics. First, agents have subjective beliefs instead of rational expectations. They learn about the inflation target set by the central bank and their expectations may become anchored or unanchored over time, given the state of the economy. Second, agents face time-varying risk aversion. The model has one main prediction: the sensitivity of the term structure to inflation surprises is not only time-varying, but state-dependent.

The Heath-Jarrow-Morton (HJM) model represents the latest in powerful arbitrage-free technology for modeling the term structure and managing interest rate risk. Yet risk management strategies in the form of immunization portfolios using duration, convexity, and M-square are still widely used in bond portfolio management today. This study addresses the question of how traditional risk measures and immunization strategies perform when the term structure evolves in the HJM manner. Using Monte Carlo simulation, I analyze four HJM volatility structures, four initial term structure shapes, three holding periods, and two traditional immunization approaches (duration-matching and duration-and-convexity-matching). I also examine duration and convexity measures derived specifically for the HJM framework. In addition I look at whether portfolios should be constructed randomly, by minimizing their M-squares or using barbell or bullet structures. I assess immunization performance according to three criteria. One of these criteria corresponds to active portfolio management, and the other two correspond to passive portfolio management. Under active portfolio management, an asset portfolio is successfully immunized if its holding period return is greater than or equal to the holding period return of the liability portfolio. Under passive portfolio management, the closer the returns of the asset portfolio to the returns of the liability portfolio, the better the immunization performance. The results of the study suggest that, under the active portfolio management criterion, and with the duration matching strategy, HJM and traditional duration measures have similar immunization performance when forward rate volatilities are low. There is a substantial deterioration in the immunization performance of traditional risk measures when there is high volatility. This deterioration is not observed with HJM duration measures. These results could be due to two factors. Traditional risk measures could be poor risk measures, or the duration matching strategy is not the most appropriate immunization approach when there is high volatility because yield curve shifts would often be large. Under the active portfolio management criterion and with the duration and convexity matching strategy, the immunization performance of traditional risk measures improves considerably at the high volatility segments of the yield curve. The improvement in the performance of the HJM risk measures is not as dramatic. The immunization performance of traditional duration and convexity measures, however, deteriorates at the low volatility segments of the yield curve. This deterioration is not observed when HJM risk measures are used. Overall, with the duration and convexity matching strategy, the immunization performance of portfolios matched with traditional risk measures is very close to that of portfolios matched with the HJM risk measures. This result suggests that the duration and convexity matching approach should be preferred to duration matching alone. Also the result shows that the underperformance of traditional risk measures under high volatility is not due to their being poor risk measures, but rather due to the reason that the duration matching strategy is not an appropriate immunization approach when there is high volatility in the market. Under the passive portfolio management criteria, the performances of traditional and HJM measures are similar with the duration matching strategy. Less than 29% of the duration matched portfolios have returns within one basis point of the target yield, whereas almost all are within 100 basis points of the target yield. These results suggest that the duration matching strategy might not be sufficient to generate cash flows close to those of the target bond. The duration measure assumes a linear relation between the bond price and the yield change, and the nonlinearities that are not captured by the duration measure might be important. When the duration and convexity matching strategy is used, more than 36% of the portfolios are within one basis point of the target with HJM risk measures. This dramatic improvement in the immunization performance of HJM measures is not guaranteed for traditional risk measures. In fact, there are certain cases in which the performance of traditional risk measures deteriorates with the duration and convexity matching strategy. In this respect, choosing the correct risk measure is more important than the immunization strategy when passive portfolio management is pursued. Under active portfolio management criterion, there is no significant difference among bullet, barbell, minimum M-square, and random portfolios with both duration matching and duration and convexity matching strategies. Under the passive portfolio management criterion, bullet portfolios produce closer returns to the target for short holding periods when the duration matching strategy is used. With the duration and convexity matching strategy, bullet, barbell and minimum M-square portfolios produce closer returns to the target for short holding periods. Random portfolios perform as well as bullet, barbell and minimum M-square portfolios for medium to long holding periods. These results suggest that when the duration matching strategy is used, bullet portfolios are preferable to other portfolio formation strategies for short holding periods. When the duration and convexity matching strategy is used, no portfolio formation strategy is better than the other. Under the active portfolio management criterion, minimum M-square portfolios are successfully immunized under each yield curve shape and volatility structure considered. Under the passive portfolio management criterion, minimum M-square portfolios perform better for short holding periods, and their performance deteriorates as the holding period increases, irrespective of the volatility level. This suggests that the performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. Therefore, minimum M-square portfolios would be preferred in the markets when there are large changes in volatility. Overall, the results of the study suggest that, under the active portfolio management criterion and with the duration matching strategy, traditional duration measures underperform their HJM counterparts when forward rate volatilities are high. With the duration and convexity matching strategy, this underperformance is not as dramatic. Also no particular portfolio formation strategy is better than the other under the active portfolio management criterion. Under the passive portfolio management criterion, the duration matching strategy is not sufficient to generate cash flows closer to those of the target bond. The duration and convexity matching strategy, however, leads to substantial improvement in the immunization performance of the HJM risk measures. This improvement is not guaranteed for the traditional risk measures. Under the passive portfolio management criterion, bullet portfolios are preferred to other portfolio formation strategies for short holding periods. For medium to long holding periods, however, the portfolio formation strategy does not significantly affect immunization performance. Also, the immunization performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. / Ph. D.